992:
10 digits without telling him. Here, we use the computer to generate a random number from 1 to 10. The generated number is 7, and the 7th number of the first 10 digits in the table is also 7. Suppose that this is the number that the second student picks. She then counts 7 places along the list, starting from the number next to 7. The count stops at (another) 7. She then counts 7 places along the list, again. This time the count stops at 3. She then counts 3 places along the list, and so on. In the case that the count stops at 0, the student then counts 10 places on the list. The student's counts are underlined in Table 10.1. The trick is that these are all secretly done behind the professor, who then turns around and points out where the student's counts finally ends, which is the last 9 in the table.
818:(1925–2006). The nature of these Kruskal sequences is that they converge exponentially fast, and for N=52 there is already more than 90% chance that the two randomly started sequences converge at the end of the deck, that is the magician and the spectator independently arrive at the same last key card. I saw the trick demonstrated at one conference, but didn't know that these convergent, linked list-like, series are so common. Almost any books can be used to show that. Skip a number of words equal to the number of letters in a key word. By the end of the third line you normally converge to the same sequence forever after, no matter which word in the top line you start with.
174:, under certain conditions, is typically independent of the input. A simplified version using the hands of a clock is as follows. A volunteer picks a number from one to twelve and does not reveal it to the magician. The volunteer is instructed to start from 12 on the clock and move clockwise by a number of spaces equal to the number of letters that the chosen number has when spelled out. This is then repeated, moving by the number of letters in the new number. The output after three or more moves does not depend on the initially chosen number and therefore the magician can predict it.
156:
1423:. The instructor asks a student to write 100 random digits from 0 to 9 on the blackboard. Another student chooses one of the first 10 numbers and does not tell the instructor. If that digit is 7 say she counts 7 places along the list, notes the digit at that location, and continues the process. If the digit is 0 she counts 10. A possible sequence is underlined on the list below: 3 4
1446:
2 3 . . . The trick is that, without knowing the student's first digit, the instructor can point to her final stopping position. To this end, he picks the first digit, and forms his own sequence in the same manner as the student and announces his stopping position. He makes an error if
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in
Princeton. Kruskal came up afterwards, full of enthusiasm for the lecture, and asked: "How come I never heard of you? That was wonderful!" The kid tried to remind Kruskal of their history. Kruskal denied it but the kid still has the letter. This was one of the few times that Martin Kruskal's keen
991:
used to entertain the students in his probability class with the following counting trick. A professor asks a student to write 100 random digits from 0 to 9 on the blackboard. Table 10.1 shows 100 such digits generated by a computer. The professor then asks another student to choose one of the first
2839:(1976-12-01). Written at Chicago, Illinois, US. Hudson, Charles (ed.). "Approach & Uses for the "Kruskal Kount" / First Presentation Angle / Second Presentation Angle - Checking the Deck / Third Presentation Angle - The 100% Method / Fourth Presentation Angle - "Disaster"". Card Corner.
1613:) that went roughly: "It's true, Martin. You don't know about mathematics. No one with this kid's limited background could ever make it through a serious math department." Kruskal went on to explain what has come to be known as the Kruskal principle. This is a broadly useful new principle in
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of cards or numbers is traversed in a linked-list manner, that is when you see a value in a list of integers, you use it to determine the position of the next number in a sequence, and you repeat that until the list ends. This is the basis of a
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The trick is performed with cards, but is more a magical-looking effect than a conventional magic trick. The magician has no access to the cards, which are manipulated by members of the audience. Thus
3683:
3682:
Lamprecht, Daniel; Dimitrov, Dimitar; Helic, Denis; Strohmaier, Markus (2016-08-17). "Evaluating and
Improving Navigability of Knowledge: A Comparative Study of Eight Language Editions".
1601:
and, after graduation, the kid eventually returned to
Harvard as a professor. One other tale about Martin's letter. It was sent to a long list of graduate schools. He got a reply from
1479:
557:
1581:, Martin was one of our letter writers. There are heart-warming stories here. Martin's letter of recommendation said something like: "I don't know a lot about mathematics but
2787:
2468:
2506:. Survey of Recent East European Mathematical Literature. Vol. 3. Translated by Whaland, Jr., Norman D.; Titelbaum, Olga A. (1 ed.). Boston, Massachusetts, US:
1907:
1842:
1734:
2671:. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Vol. II (122). Translated by
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2581:. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Vol. I (121). Translated by
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1676:(6). Department of Business Information, Faculty of Information Management, Osaka University of Economics, Osaka, Japan: Academic Publications, Ltd.: 983–992.
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has turned dozens of innocent youngsters into math professors and thousands of math professors into innocent youngsters. We are living proof; Martin nurtured
3677:
749:
MacTier, Arthur F. (2000). "Chapter 6: Kruskal
Principle (Extraordinary Coincidence) / Chapter 7: Kraus Principle (The Magic of 52, Magical Coincidence II)".
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with a magician correctly guessing the final number in a seemingly hidden/random sequence computed by a spectator in his/her mind (but using a given
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statistics professor and keen amateur magician, was on the admissions committee and let the kid into
Harvard. Fred became the kid's
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17:
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Bosko, Lindsey R. (2011). Written at
Department of Mathematics, North Carolina State University, Raleigh, North Carolina, US.
3122:(7). Advanced Modeling and Applied Computing Laboratory and Department of Mathematics, The University of Hong Kong, Hong Kong:
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from
Harvard in 1974, so Kruskal's reply must have been between 1971 and 1974 the latest. Gardner published the trick in
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1169:; Hsu, Justin; Stefanesco, Léo; Strub, Pierre-Yves (2017-07-12) . "Relational Reasoning via Probabilistic Coupling".
492:
390:
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when the length of element is used to create a jump to the next element are called Dynkin–Kruskal sequences, after
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807:
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585:
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228:
213:
140:
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132:
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1998:
1948:
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1288:. The Wadsworth & Brooks/Cole Statistics/Probability Series (1 ed.). Pacific Grove, California, US:
545:
458:
3251:. Proceedings of the forty-first annual ACM symposium on Theory of computing (STOC 2009). pp. 553–560.
314:(February 1978). "On checker jumping, the Amazon game, weird dice, card tricks and other playful pastimes".
96:
in the early 1970s as a side-product while working on another problem. It was published by
Kruskal's friend
3741:
3608:. Proceedings of the 18th IACR International Conference on Practice and Theory in Public-Key Cryptography.
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2931:
1997:
Kraus, Alexander F. (1993). "Sum Total (Solution)". In Ransom, Tom; Field, Matthew; Phillips, Mark (eds.).
685:
3660:"PDCA and the Roads to Rome: Can a lean purist and a Six Sigma purist reach the same answer to a problem?"
1947:
Kraus, Alexander F. (1993). "Sum Total (Problem)". In Ransom, Tom; Field, Matthew; Phillips, Mark (eds.).
814:(1924–2014), a Russian-American mathematician, who mentioned them in his work, and American mathematician
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2427:
1758:
1590:
2304:
Towards
Integral Binary Execution: Implementing Oblivious Hashing Using Overlapped Instruction Encodings
668:
2862:
Hudson, Charles (1977-10-01). Written at
Chicago, Illinois, US. "The Kruskal Principle". Card Corner.
2100:
1526:
770:"Codes for PHYD57 Advanced Computing in Physics, UTSC: Dynkin–Kruskal count - convergent Markov chains"
532:
124:
3472:(2014-07-10). Written at Vrije Universiteit Amsterdam, Amsterdam, Netherlands. Dietrich, Sven (ed.).
3099:
3123:
3053:
2899:
2754:
2660:
2570:
2536:Математические беседы: Задачи о многоцветной раскраске / Задачи из теории чисел / Случайные блуждания
2507:
2493:
2210:
1407:
988:
321:
128:
81:
3243:
2500:(1963). Written at University of Moscow, Moscow, Russia. Putnam, Alfred L.; Wirszup, Izaak (eds.).
2310:. Proceedings of the 9th workshop on Multimedia & Security (MM&Sec '07). Dallas, Texas, US:
457:. Canadian Mathematical Society Conference Proceedings. Vol. 20. Providence, Rhode Island, US:
3792:
2320:
1517:"Chapter 10. Stars Of Mathematical Magic (And Some Of The Best Tricks In The Book): Martin Gardner"
1051:
1019:
676:
208:
2043:
Ransom, Tom; Katz, Max (1993). "Sum More". In Ransom, Tom; Field, Matthew; Phillips, Mark (eds.).
589:
2829:
2563:
2511:
2417:
1399:
1379:
1318:
1281:
980:
438:
272:
223:
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2238:(2009) . "The Kruskal Count". In Brams, Stephen; Gehrlein, William V.; Roberts, Fred S. (eds.).
1861:
Braunmüller, Rudolf, ed. (January 1984). "Das Kruskal-Prinzip" [The Kruskal Principle].
104:
in 1975. This is related to a similar trick published by magician Alexander F. Kraus in 1957 as
4022:
3897:
3331:
2562:). It is based on seminars held at the School Mathematics Circle in 1945/1946 and 1946/1947 at
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2227:
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1795:
203:
183:
85:
28:
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2955:
2802:(x+237 pages) (NB. This is a corrected translation of the first Russian edition published as "
2734:(viii+274+2 pages) (NB. This was originally published in Russian as "Markovskie prot︠s︡essy" (
2088:
1516:
1322:
912:
843:
765:
434:
4012:
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3602:
Collision of Random Walks and a Refined Analysis of Attacks on the Discrete Logarithm Problem
3600:
3483:
International Conference on Detection of Intrusions and Malware, and Vulnerability Assessment
2054:
2008:
1958:
1754:
1750:
1582:
1568:
1508:
597:
373:
260:
2092:
1525:(4th printing of 1st ed.). Princeton, New Jersey, US & Woodstock, Oxfordshire, UK:
450:
3828:
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3428:
3341:. Modules and Monographs in Undergraduate Mathematics and its Applications (UMAP) Project.
2999:
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2058:
2012:
1962:
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1307:
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is not possible. Rather the effect is based on the mathematical fact that the output of a
8:
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3832:
2418:"How to Do the Math Magic Trick That Will Impress Everyone You Know - Here's the secret"
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1577:), found time to occasionally help with homework, and, when the time came to apply for
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1127:
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891:
799:
751:
Card Concepts - An Anthology of Numerical & Sequential Principles Within Card Magic
713:
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333:
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2240:
The Mathematics of Preference, Choice and Order. Essays in Honor of Peter J. Fishburn
2179:
2169:
2139:(xii+235 pages) (NB. The book contains a significant number of typographical errors:
2122:
2104:
2049:. Vol. 1. Lyons, Pat Patterson (illustrations) (1 ed.). Washington DC, US:
2003:. Vol. 1. Lyons, Pat Patterson (illustrations) (1 ed.). Washington DC, US:
1953:. Vol. 1. Lyons, Pat Patterson (illustrations) (1 ed.). Washington DC, US:
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Kruskal's Principle and Collision Time for Monotone Transitive Walks on the Integers
3274:
2753:
2347:
2279:
1447:
the coupling time is larger than 100. Numerical computation done by one of Dynkin's
1157:
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1096:
Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages
3854:
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689:
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442:
3035:; Lee, Yiu-Fai (September 2005) . "A Random Walk on a Circular Path". Miscellany.
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451:
264:
167:
3889:
called the Kruskal Count so we have dubbed the phenomenon as "Kruskal effect".
3625:
3498:
3179:
1327:. The Duxbury Advanced Series in Statistics and Decision Sciences (3 ed.).
971:, one of the classroom examples that struck him the most was given by Professor
3423:
2885:
2402:
2062:
2016:
1966:
1824:
1790:
1766:
1598:
1564:
372:(1997). "Chapter 19. Sicherman Dice, the Kruskal Count and Other Curiosities".
369:
354:
311:
256:
198:
144:
97:
3930:
3900:(2023-08-22) . "Constructions and bounds for codes with restricted overlaps".
3131:
3061:
2696:
2610:
1935:
Kraus, Alexander F. (December 1957). Lyons, Philip Howard (ed.). "Sum Total".
1865:(in German). Vol. 10, no. 3 & 4. Munich, Germany. pp. 125–.
1571:, published some of our mathematical findings to give a first publication (in
987:). A modified (and expanded) version is given below. Example 10.1. Professor
930:
861:
4001:
3918:(17 pages) (NB. This source does not mention Dynkin or Kruskal specifically.)
3850:
3768:
3749:(Thesis). Lund, Sweden: Department of Electrical and Information Technology,
3524:
3506:
3440:
3207:
3147:
3139:
3077:
3069:
2907:
2890:
2877:
2854:
2714:
2628:
2434:
2035:
Ransom, Tom; Katz, Max (March 1958). Lyons, Philip Howard (ed.). "Sum More".
1697:
1689:
1406:"]: "Example. A coupling card trick. The following demonstration used by
956:
938:
879:
811:
701:
622:
553:
476:
446:
362:
329:
120:
77:
3700:
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1170:
1166:
1162:
1113:
1091:
1087:
1083:
1040:
1008:
908:
839:
430:
115:
Besides uses as a card trick, the underlying phenomenon has applications in
3868:
2888:(September 1998). "Ten Amazing Mathematical Tricks". Gardner's Gatherings.
2771:
2152:(2009) . "Kapitel 12 - Numerologie und Kartentricks: Das Kruskal-Prinzip".
1989:. No. 13. Toronto, Ontario, Canada. pp. 13–16. Part 2 (Solution).
1985:
Kraus, Alexander F. (March 1958). Lyons, Philip Howard (ed.). "Sum Total".
1681:
1622:
1522:
Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks
786:
193:
171:
116:
42:
3469:
3368:
3346:
3296:
3112:
3042:
2828:) with the assistance of the authors. It is based on lectures held at the
2672:
2582:
2118:
1666:
1368:
614:
155:
3410:
Humble, Steve "Dr. Maths" (September 2012) . Written at Kraków, Poland.
3108:
International Journal of Mathematical Education in Science and Technology
3038:
International Journal of Mathematical Education in Science and Technology
2809:
2388:
1893:
1876:
1828:
1807:
753:(1 ed.). London, UK: Lewis Davenport Limited. pp. 34–38, 39–46.
255:
explained the trick, which later became known as Kruskal's principle, to
218:
101:
41:"Dynkin's card trick" redirects here. For optimal stopping problems, see
2924:
Haigh, John (1999). "7. Waiting, waiting, waiting: Packs of cards (2)".
2915:
337:
3886:
3397:
2750:) in 1963 and translated to English with the assistance of the author.)
2144:
1625:
1614:
1586:
1411:
795:
709:
89:
3896:
Blackburn, Simon Robert; Esfahani, Navid Nasr; Kreher, Donald Lawson;
3841:
2533:(NB. This is a translation of the first Russian edition published as "
3685:
Proceedings of the 12th International Symposium on Open Collaboration
3009:
2741:
2464:
2252:
1939:. No. 12. Toronto, Ontario, Canada. p. 7. Part 1 (Problem).
1774:
1762:
1104:
3192:(2 & 3). Missoula, Montana, US: University of Montana: 327–336.
1609:(a major mathematician who was most well-known for his discovery of
693:
3912:
3823:
2836:
2292:
2290:
1189:
803:
3790:
3257:
2126:
1544:
887:
375:
Penrose Tiles to Trapdoor Ciphers ... and the return of Mr. Matrix
359:
Penrose Tiles to Trapdoor Ciphers ... and the return of Mr. Matrix
3935:
3801:"Sensorless Pose Determination Using Randomized Action Sequences"
2160:] (in German). Translated by Zillgitt, Michael (1 ed.).
2067:(319 pages) (NB. Volume 1 of a three-volume hardcover reprint of
2021:(319 pages) (NB. Volume 1 of a three-volume hardcover reprint of
1971:(319 pages) (NB. Volume 1 of a three-volume hardcover reprint of
1921:(381 pages) (NB. Volume 3 of a three-volume hardcover reprint of
1855:(381 pages) (NB. Volume 3 of a three-volume hardcover reprint of
1610:
1078:
1076:
684:(500). Tidmarsh Cottage, Manor Farm Lane, Tidmarsh, Reading, UK:
3681:
3475:
Instruction-Level Steganography for Covert Trigger-Based Malware
2783:
2722:
2636:
2519:
2287:
2222:
2220:
921:. Springer Texts in Statistics (2 ed.). Cham, Switzerland:
400:
27:"Kruskal's principle" redirects here. For Kruskal's method, see
2242:. Studies in Choice and Welfare. Berlin / Heidelberg, Germany:
2158:
Impossible? Surprising Solutions to Counterintuitive Conundrums
2095:
Impossible? Surprising Solutions to Counterintuitive Conundrums
915:. Written at University of California, Davis, California, US.
846:. Written at University of California, Davis, California, US.
605:(4). Tidmarsh Cottage, Manor Farm Lane, Tidmarsh, Reading, UK:
3895:
1073:
484:
34:"Sum Total" redirects here. For the statistical quantity, see
2385:
Once Upon a Number - The Hidden Mathematical Logic of Stories
2217:
1172:
Logic for Programming, Artificial Intelligence, and Reasoning
280:
80:
concept originally demonstrated by the Russian mathematician
2770:. Translated by Wood, James S. (1 ed.). New York, US:
2761:(1969) . Written at University of Moscow, Moscow, Russia.
2663:(1965) . Written at University of Moscow, Moscow, Russia.
2573:(1965) . Written at University of Moscow, Moscow, Russia.
2543:
852:. Springer Texts in Statistics (1 ed.). New York, US:
268:
3791:
Mannam, Pragna; Volkov, Jr., Alexander; Paolini, Robert;
2296:
1563:
A blurb that appears on one of his books says: Warning:
1478:(in German). Ulm, Germany: University of Ulm. p. 7.
1451:
show that the probability of error is approximately .026.
1290:
Wadsworth & Brooks/Cole Advanced Books & Software
381:. Spectrum Series (Revised ed.). Washington DC, US:
259:
in a reply to a letter Gardner had sent him to recommend
2569:
2039:. No. 13. Toronto, Ontario, Canada. pp. 17–18.
1589:
of the past ten years. You ought to give him a chance."
1161:
3743:
On Offensive and Defensive Methods in Software Security
3595:(2015-03-15) . Written at Gaithersburg, Maryland, US.
2191:
2226:
1082:
1045:"Probabilistic couplings for cryptography and privacy"
1013:"Probabilistic couplings for cryptography and privacy"
2071:
magazine numbers 1 (June 1955) – 15 (December 1958).)
2025:
magazine numbers 1 (June 1955) – 15 (December 1958).)
1975:
magazine numbers 1 (June 1955) – 15 (December 1958).)
1885:. Vol. 10, no. 8. Teaneck, New Jersey, US:
1816:. Vol. 10, no. 9. Teaneck, New Jersey, US:
1799:. Vol. 10, no. 8. Teaneck, New Jersey, US:
1662:
International Journal of Pure and Applied Mathematics
1247:"Probabilistic Couplings for Probabilistic Reasoning"
1501:
1378:. Corvallis, Oregon, US: Department of Mathematics,
1092:"Coupling Proofs are Probabilistic Product Programs"
913:"Chapter 10 Stochastic Processes; 10.1 Introduction"
844:"Chapter 10 Stochastic Processes; 10.1 Introduction"
449:; Jörgenson, Loki; Corless, Robert "Rob" M. (eds.).
3614:International Association for Cryptologic Research
2956:"7. Waiting, waiting, waiting: Packs of cards (2)"
2664:
2574:
2461:"Graph Based Model for Software Tamper Protection"
1859:magazine volumes 9 (November 1973) – 10 (1977).);
607:International Association for Cryptologic Research
3347:Consortium For Mathematics & Its Applications
2868:. Vol. 57, no. 10. Bluffton, Ohio, US:
2845:. Vol. 56, no. 12. Bluffton, Ohio, US:
2197:
1904:L & L Publishing - Quality Magical Literature
1839:L & L Publishing - Quality Magical Literature
1644:
1642:
1640:
1638:
1363:
1361:
1090:; Hsu, Justin; Strub, Pierre-Yves (2016-11-07) .
320:. Mathematical Games. Vol. 238, no. 2.
3999:
3590:
3554:
3234:
2503:Random Walks (Mathematical Conversations Part 3)
2028:
1925:magazine volumes 9 (November 1973) – 10 (1977).)
1466:
1464:
659:
657:
655:
580:
578:
521:"Monte Carlo Methods for Index Computation (mod
3245:How Long Does it Take to Catch a Wild Kangaroo?
2825:Теория вероятностей и математическая статистика
2452:
1321:(2005). "Example 5.2. A coupling card trick.".
1312:(x+453 pages) (NB. This can be found quoted in
1276:
1274:
422:
241:
3815:Multidisciplinary Digital Publishing Institute
2820:Probability Theory and Mathematical Statistics
2687:(1 ed.). New York, US / Berlin, Germany:
2597:(1 ed.). New York, US / Berlin, Germany:
1991:(4 pages) (NB. The first part can be found in
1941:(1 page) (NB. The second part can be found in
1635:
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1003:
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2745:
2735:
2557:
2547:
2534:
2079:
2077:
1617:. A few years later, the kid lectured at the
1461:
1410:in his probability class is a variation of a
1351:(497 pages) (NB. This can be found quoted in
652:
590:"Kangaroos, Monopoly and Discrete Logarithms"
575:
3467:
3100:"On Convergent Probability of a Random Walk"
2409:
1783:
1769:who had earlier written about their mother,
1719:
1454:(45 pages) (NB. This can be found quoted in
1271:
834:
832:
3379:. Lausanne, Switzerland: Data Science Lab,
2369:
2154:Das gibts doch nicht – Mathematische Rätsel
1869:
1860:
1473:"Vorstellung der Kopplung bei Markovketten"
1240:
1238:
998:
739:
544:, Taplow Court, Maidenhead, Berkshire, UK:
506:
344:
301:
3881:The phenomenon, while also reminiscent of
2458:
2074:
2042:
2034:
1978:
1928:
1749:had two mathematically inclined brothers,
1733:. Indianapolis, Indiana, US. p. 316.
764:
428:
3911:
3858:
3840:
3822:
3739:
3256:
3197:
2381:"An old card trick and new Biblical hoax"
2319:
2297:Jacob, Matthias; Jakubowski, Mariusz H.;
2251:
2099:(1 ed.). Princeton, New Jersey, US:
1648:
1495:
1367:
1352:
1188:
1103:
829:
3939:(Video). Alchemist Cafe, Dublin, Ireland
3740:Jämthagen, Christopher (November 2016).
3381:École Polytechnique Fédérale de Lausanne
3349:, Inc. (COMAP): 199–236. UMAP Unit 808.
3093:
3031:
2961:Taking Chances: Winning with Probability
2927:Taking Chances: Winning with Probability
2459:Jakubowski, Mariusz H. (February 2016).
1470:
1455:
1235:
441:, Burnaby, British Columbia, Canada. In
154:
3903:IEEE Transactions on Information Theory
3178:Humble, Steve "Dr. Maths" (July 2008).
3005:Puzzlers' Tribute: A Feast for the Mind
2964:(Reprint of 2nd ed.). Oxford, UK:
2884:
2764:Markov Processes: Theorems and Problems
2415:
2162:Spektrum Akademischer Verlag Heidelberg
1902:. Vol. 3. Tahoma, California, US:
1837:. Vol. 3. Tahoma, California, US:
1823:
1789:
1725:
1415:
1403:
1317:
1280:
984:
748:
663:
584:
515:
368:
353:
310:
284:
267:. Diaconis graduated in 1971, earned a
14:
4000:
3928:
3416:"Mathematics in the Streets of Kraków"
3409:
3177:
2870:International Brotherhood of Magicians
2861:
2847:International Brotherhood of Magicians
2659:
2375:
1892:
1875:
1810:, ed. (July 1975). "Cross-Cut Force".
1806:
1793:(June 1975). "The Kruskal Principle".
1039:
1007:
918:Large Sample Techniques for Statistics
849:Large Sample Techniques for Statistics
3329:
3295:
2953:
2923:
2835:
2148:
2083:
1996:
1992:
1984:
1946:
1942:
1934:
1879:(June 1975). "Kruskal Phone Effect".
1827:(1993) . "The Kruskal Principle". In
1313:
907:
838:
3973:
3657:
3612:. Berlin & Heidelberg, Germany:
3427:. No. 85. Zürich, Switzerland:
3367:
2989:
2805:Теоремы и задачи о процессах Маркова
2051:Richard Kaufman & Alan Greenberg
2005:Richard Kaufman & Alan Greenberg
1955:Richard Kaufman & Alan Greenberg
1899:The Pallbearers Review: Volumes 9–10
1834:The Pallbearers Review: Volumes 9–10
1373:"From Markov Chains to Gibbs Fields"
854:Springer Science+Business Media, LLC
3693:Association for Computing Machinery
2896:Mathematical Association of America
2759:Yushkevish , Aleksandr Adol'fovich
2312:Association for Computing Machinery
1244:
542:Plessey Telecommunications Research
383:Mathematical Association of America
24:
3929:Humble, Steve "Dr. Maths" (2010).
3404:. It's called the "Kruskal Count"
3185:The Montana Mathematics Enthusiast
2849:. pp. 82, 83, 83, 84, 85–87.
2486:
1863:intermagic - Ein Magisches Journal
1494:(1+9 pages) (NB. This work quotes
25:
4034:
3922:
3610:Lecture Notes in Computer Science
3491:Springer International Publishing
3487:Lecture Notes in Computer Science
3345:(3). Bedford, Massachusetts, US:
2818:) in 1967 as part of a series on
2559:Библиотека математического кружка
2554:Library of the Mathematics Circle
2498:Uspenskii , Vladimir Andreyevich
1896:(1993) . "Kruskal Phone Effect".
1404:Probability: Theory and Examples.
1177:Lecture Notes in Computer Science
84:in the 1950s or 1960s discussing
3952:"Mathematical Card Trick Source"
2416:Delbert, Caroline (2020-02-27).
1324:Probability: Theory and Examples
1286:Probability: Theory and Examples
1179:. Vol. 9450. Suva, France:
147:, object alignment, and others.
141:variable-length instruction sets
3986:from the original on 2023-09-10
3962:from the original on 2023-09-04
3885:, is similar to an interesting
3778:from the original on 2023-08-26
3728:from the original on 2023-09-04
3666:from the original on 2023-09-07
3645:from the original on 2023-09-03
3618:Springer Science+Business Media
3578:from the original on 2023-08-22
3542:from the original on 2023-08-26
3450:from the original on 2023-09-02
3387:from the original on 2022-05-23
3356:from the original on 2023-08-19
3317:from the original on 2023-08-19
3284:from the original on 2023-08-20
3222:from the original on 2023-09-03
3165:from the original on 2023-09-02
3014:Taylor & Francis Group, LLC
2793:from the original on 2023-09-06
2552:) in March 1952 as Number 6 in
2471:from the original on 2019-10-31
2441:from the original on 2021-10-19
2357:from the original on 2018-09-04
2209:. Murray Hill, New Jersey, US:
2166:Springer Science+Business Media
1910:from the original on 2023-09-10
1845:from the original on 2023-09-10
1737:from the original on 2023-08-19
1707:from the original on 2023-08-19
1485:from the original on 2023-09-01
1471:Weinhold, Leonie (2011-05-13).
1389:from the original on 2023-09-01
1319:Durrett, Richard "Rick" Timothy
1282:Durrett, Richard "Rick" Timothy
1259:from the original on 2023-08-19
1223:from the original on 2023-08-19
1138:from the original on 2023-08-19
1061:from the original on 2023-08-19
1029:from the original on 2023-08-19
776:from the original on 2023-08-20
727:from the original on 2023-08-18
640:from the original on 2023-08-18
563:from the original on 2013-05-03
540:(143). Mathematics Department,
410:from the original on 2023-08-19
229:Knowledge:Getting to Philosophy
3898:Stinson, Douglas "Doug" Robert
2228:Lagarias, Jeffrey "Jeff" Clark
2199:Lagarias, Jeffrey "Jeff" Clark
1731:"Foshee Magically Interpreted"
1619:Institute for Defense Analyses
1329:Thomson Brooks/Cole Publishing
967:During the author's time as a
923:Springer Nature Switzerland AG
133:control-flow resynchronization
92:by the American mathematician
88:effects and rediscovered as a
13:
1:
3433:European Mathematical Society
3332:"Cards, Codes, and Kangaroos"
2776:Plenum Publishing Corporation
2089:"Chapter 12: Two Card Tricks"
979:. The example was taken from
546:American Mathematical Society
459:American Mathematical Society
294:
150:
3691:. OpenSym, Berlin, Germany:
3658:Jose, Harish (2016-06-14) .
2992:"A Labyrinth in a Labyrinth"
2966:Oxford University Press Inc.
2932:Oxford University Press Inc.
2755:Dynkin , Evgenii Borisovich
2571:Dynkin , Evgenii Borisovich
2494:Dynkin , Evgenii Borisovich
2262:10.1007/978-3-540-79128-7_23
1765:. All three were friends of
1199:10.1007/978-3-662-48899-7_27
686:The Mathematical Association
249:Diaconis & Graham (2012)
214:Pollard's kangaroo algorithm
7:
4018:Number theoretic algorithms
3931:"Dr. Maths Randomness Show"
3626:10.1007/978-3-662-46447-2_6
3499:10.1007/978-3-319-08509-8_3
2894:. Vol. 6, no. 1.
2428:Hearst Magazine Media, Inc.
1569:a runaway fourteen-year-old
177:
10:
4039:
3879:. Article 154. p. 2:
3489:. Egham, UK; Switzerland:
3124:Taylor & Francis, Ltd.
3054:Taylor & Francis, Ltd.
2930:(1 ed.). Oxford, UK:
2900:Taylor & Francis, Ltd.
2661:Dynkin, Evgenii Borisovich
2211:AT&T Bell Laboratories
2101:Princeton University Press
1527:Princeton University Press
1513:Graham, Ronald "Ron" Lewis
533:Mathematics of Computation
125:software tamper protection
40:
33:
26:
3974:Behr, Denis, ed. (2023).
3813:(2). Basel, Switzerland:
3793:Chirikjian, Gregory Scott
3373:"Knowledge's fixed point"
3132:10.1080/00207390600712299
3062:10.1080/00207390500064254
2824:
2814:
2804:
2746:
2736:
2697:10.1007/978-3-662-25360-1
2611:10.1007/978-3-662-00031-1
2558:
2548:
2535:
2508:The University of Chicago
1841:. pp. 967–970, 985.
1585:invented two of the best
931:10.1007/978-3-030-91695-4
862:10.1007/978-1-4419-6827-2
806:. Random sequences that
322:Scientific American, Inc.
129:code self-synchronization
82:Evgenii Borisovich Dynkin
4008:Recreational mathematics
3396:it turns out there is a
2301:(20–21 September 2007).
2046:ibidem - P. Howard Lyons
2000:ibidem - P. Howard Lyons
1950:ibidem - P. Howard Lyons
1629:insight led him astray!
1398:Here we will quote [
1052:IMDEA Software Institute
1020:IMDEA Software Institute
677:The Mathematical Gazette
435:"On Kruskal's Principle"
234:
209:Overlapping instructions
18:Dynkin's card trick
3701:10.1145/2957792.2957813
3267:10.1145/1536414.1536490
3199:10.54870/1551-3440.1111
2986:(4 of xiv+373+17 pages)
2830:Moscow State University
2677:Greenberg, Vida Lazarus
2587:Greenberg, Vida Lazarus
2564:Moscow State University
2512:D. C. Heath and Company
2330:10.1145/1288869.1288887
2299:Venkatesan, Ramarathnam
1654:"The Kruskal principle"
1380:Oregon State University
1114:10.1145/3009837.3009896
439:Simon Fraser University
357:(1989) . "Chapter 19".
273:mathematical statistics
224:Self-synchronizing code
62:Dynkin's counting trick
1923:The Pallbearers Review
1882:The Pallbearers Review
1857:The Pallbearers Review
1813:The Pallbearers Review
1796:The Pallbearers Review
1682:10.12732/ijpam.v85i6.1
1509:Diaconis, Persi Warren
1369:Kovchegov, Yevgeniy V.
1252:(Thesis). p. 34.
669:"Kruskal's Card Trick"
204:Geometric distribution
184:Coupling (probability)
163:
3797:Mason, Matthew Thomas
2990:Bean, Gordon (2002).
2954:Haigh, John (2009) .
2055:Kaufman and Greenberg
2009:Kaufman and Greenberg
1959:Kaufman and Greenberg
1755:University of Chicago
1632:(2+xii+2+244+4 pages)
1529:. pp. 211–219 .
1245:Hsu, Justin (2018) .
615:10.1007/s001450010010
598:Journal of Cryptology
385:. pp. 265–280 .
158:
137:variable-length codes
3787:(1+xvii+1+152 pages)
3620:. pp. 127–149.
3429:EMS Publishing House
3016:. pp. 103–106.
2902:pp. 13–15, 26.
2685:Majone, Giandomenico
2681:Maitra, Ashok Prasad
2603:Academic Press, Inc.
2595:Majone, Giandomenico
2591:Maitra, Ashok Prasad
2314:. pp. 129–140.
2246:. pp. 371–391.
2236:Vanderbei, Robert J.
2203:Vanderbei, Robert J.
2168:. pp. 128–135.
2103:. pp. 131–140.
2065:). pp. 258–259.
2059:Hermetic Press, Inc.
2019:). pp. 255–258.
2013:Hermetic Press, Inc.
1963:Hermetic Press, Inc.
1887:L & L Publishing
1818:L & L Publishing
1801:L & L Publishing
1561:. pp. 211–212:
1183:. pp. 387–401.
1098:. pp. 161–174.
925:. pp. 339–341.
856:. pp. 317–319.
816:Martin David Kruskal
461:. pp. 407–411.
94:Martin David Kruskal
58:Dynkin–Kruskal count
36:Total sum of squares
3976:"Kruskal Principle"
3883:contraction mapping
3833:2019Entrp..21..154M
3493:. pp. 41–50 .
3468:Andriesse, Dennis;
3435:. pp. 20–21 .
3400:that works exactly
3105:. Classroom notes.
2737:Марковские процессы
2667:Markov Processes-II
2658:(xii+365+1 pages);
2530:(1+9+80+9+1 pages)
2232:Rains, Eric Michael
1771:Lillian Oppenheimer
1574:Scientific American
1420:Scientific American
1165:; Espitau, Thomas;
975:in his lectures on
453:Organic Mathematics
317:Scientific American
70:coupling card trick
66:Dynkin's card trick
54:Kruskal's principle
29:Kruskal's algorithm
3954:. Close-Up Magic.
3459:The Kruscal count
3180:"Magic Card Maths"
2968:pp. 139–142.
2934:pp. 133–136.
2837:Marlo, Edward "Ed"
2577:Markov Processes-I
2377:Paulos, John Allen
1803:. pp. 967–970
1219:. hal-01246719v2.
1167:Grégoire, Benjamin
1088:Grégoire, Benjamin
977:Probability Theory
906:(xvii+610 pages);
800:well-shuffled deck
277:Harvard University
189:Discrete logarithm
164:
3980:Conjuring Archive
3842:10.3390/e21020154
3760:978-91-7623-942-1
3710:978-1-4503-4451-7
3695:. pp. 1–10.
3635:978-3-662-46446-5
3560:Tetali, Prasad V.
3412:Behrends, Ehrhard
3308:singingbanana.com
3301:"Kruskal's Count"
3240:Tetali, Prasad V.
2975:978-0-19-852663-6
2941:978-0-19-850291-3
2706:978-3-662-23320-7
2620:978-3-662-00033-5
2423:Popular Mechanics
2379:(November 1998).
2339:978-1-59593-857-2
2271:978-3-540-79127-0
2207:The Kruskal Count
2184:978-3-8274-2306-1
2175:978-3-8274-2306-1
2110:978-0-691-13131-3
1906:. pp. 970–.
1727:Farrell, Jeremiah
1650:Nishiyama, Yutaka
1553:978-0-691-15164-9
1536:978-0-691-16977-4
1449:graduate students
1347:978-0-534-42441-1
1208:978-3-662-48898-0
1050:. Madrid, Spain:
1018:. Madrid, Spain:
985:1991, p. 275
948:978-3-030-91694-7
871:978-1-4419-6826-5
785:We looked at the
766:Artymowicz, Pawel
468:978-0-8218-0668-5
443:Borwein, Jonathan
261:Persi W. Diaconis
108:and later called
16:(Redirected from
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3593:Montenegro, Ravi
3586:
3584:
3583:
3577:
3570:
3556:Montenegro, Ravi
3550:
3548:
3547:
3541:
3516:978-3-31908508-1
3480:
3461:
3456:
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3339:The UMAP Journal
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3236:Montenegro, Ravi
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3023:978-1-43986410-4
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2881:
2865:The Linking Ring
2858:
2842:The Linking Ring
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2725:. Title-No. 5105
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2647:. Title-No. 5104
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2401:. Archived from
2398:978-0-46505159-5
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2150:Havil, Julian R.
2136:
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2085:Havil, Julian R.
2081:
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1123:978-1-45034660-3
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969:graduate student
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789:, where a given
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665:Pollard, John M.
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586:Pollard, John M.
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517:Pollard, John M.
513:
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419:(1+ix+319 pages)
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324:pp. 19–32.
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3799:(2019-02-06) .
3781:
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3751:Lund University
3746:
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3591:Kijima, Shuji;
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3242:(2010-11-07) .
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3098:(2006-03-07) .
3040:
3028:(xvi+421 pages)
3024:
2980:
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2942:
2886:Gardner, Martin
2796:
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2689:Springer-Verlag
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2599:Springer-Verlag
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2487:Further reading
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2244:Springer-Verlag
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2188:(xiv+234 pages)
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2033:
2029:
1983:
1979:
1969:). p. 232.
1933:
1929:
1913:
1911:
1889:. pp. 970–
1874:
1870:
1848:
1846:
1825:Gardner, Martin
1791:Gardner, Martin
1788:
1784:
1773:, a remarkable
1744:. p. 316:
1740:
1738:
1724:
1720:
1710:
1708:
1704:
1664:
1656:
1647:
1636:
1579:graduate school
1557:
1555:
1537:
1506:
1502:
1488:
1486:
1482:
1475:
1469:
1462:
1456:Weinhold (2011)
1443:
1439:
1435:
1431:
1428:
1424:
1392:
1390:
1386:
1375:
1366:
1359:
1339:
1331:. p. 312.
1300:
1292:. p. 275.
1279:
1272:
1262:
1260:
1256:
1249:
1243:
1236:
1226:
1224:
1209:
1160:
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1081:
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1047:
1032:
1030:
1026:
1015:
1006:
999:
965:. p. 339:
961:
959:
949:
900:
898:
872:
837:
830:
791:random sequence
779:
777:
768:(2020-01-29) .
763:
759:
747:
740:
730:
728:
724:
694:10.2307/3621657
671:
662:
653:
643:
641:
637:
592:
588:(2000-08-10) .
583:
576:
566:
564:
560:
527:
514:
507:
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495:
469:
427:
423:
413:
411:
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378:
370:Gardner, Martin
355:Gardner, Martin
352:
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312:Gardner, Martin
309:
302:
297:
292:
291:
279:in 1972, and a
265:graduate school
246:
242:
237:
180:
168:sleight of hand
159:Explanation of
153:
110:Kraus principle
52:(also known as
46:
39:
32:
23:
22:
15:
12:
11:
5:
4036:
4026:
4025:
4020:
4015:
4010:
3996:
3995:
3971:
3948:
3924:
3923:External links
3921:
3920:
3919:
3893:
3788:
3759:
3753:. p. 96.
3737:
3709:
3679:
3655:
3634:
3597:Katz, Jonathan
3588:
3562:(2014-09-07).
3552:
3515:
3465:
3457:. p. 21:
3424:EMS Newsletter
3407:
3371:(2011-05-26).
3365:
3327:
3293:
3232:
3218:. Article 14.
3175:
3094:Lee, Yiu-Fai;
3091:
3029:
3022:
3008:(1 ed.).
2987:
2974:
2940:
2921:
2882:
2872:. p. 85.
2859:
2833:
2832:in 1962/1963.)
2751:
2705:
2619:
2567:
2488:
2485:
2482:
2481:
2451:
2408:
2405:on 2015-04-01.
2397:
2391:. p. 64.
2387:(1 ed.).
2368:
2338:
2321:10.1.1.69.5258
2286:
2270:
2216:
2190:
2174:
2109:
2073:
2063:Jogestja, Ltd.
2027:
2017:Jogestja, Ltd.
1977:
1967:Jogestja, Ltd.
1927:
1868:
1782:
1767:Martin Gardner
1718:
1652:(July 2013) .
1634:
1603:Martin Kruskal
1599:thesis advisor
1591:Fred Mosteller
1565:Martin Gardner
1535:
1500:
1460:
1396:. p. 22:
1382:. p. 22.
1371:(2007-10-06).
1357:
1337:
1298:
1270:
1234:
1207:
1163:Barthe, Gilles
1151:
1122:
1084:Barthe, Gilles
1072:
1043:(2016-09-13).
1041:Barthe, Gilles
1009:Barthe, Gilles
997:
995:(xv+685 pages)
947:
870:
828:
757:
755:(vi+301 pages)
738:
651:
574:
519:(July 1978) .
505:
467:
447:Borwein, Peter
437:. Written at
433:(June 1997) .
421:
391:
361:(1 ed.).
343:
299:
298:
296:
293:
290:
289:
285:Gardner (1975)
257:Martin Gardner
253:Martin Kruskal
239:
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199:Ergodic theory
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152:
149:
145:web navigation
98:Martin Gardner
74:shift coupling
9:
6:
4:
3:
2:
4035:
4024:
4023:Markov models
4021:
4019:
4016:
4014:
4011:
4009:
4006:
4005:
4003:
3985:
3981:
3977:
3972:
3961:
3958:. 2015–2017.
3957:
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3641:
3638:. LNCS 9020.
3637:
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3604:
3603:
3598:
3594:
3589:
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3553:
3538:
3535:. LNCS 8550.
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3096:Ching, Wai-Ki
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2891:Math Horizons
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2018:
2014:
2010:
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2002:
2001:
1994:
1988:
1981:
1974:
1968:
1964:
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1956:
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1944:
1938:
1931:
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1920:
1909:
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1883:
1878:
1872:
1864:
1858:
1854:
1844:
1840:
1836:
1835:
1830:
1826:
1820:. p. 985
1819:
1815:
1814:
1809:
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1798:
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1792:
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1778:
1776:
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1596:
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1385:
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1374:
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1364:
1362:
1354:
1348:
1344:
1340:
1338:0-534-42441-4
1334:
1330:
1326:
1325:
1320:
1315:
1309:
1305:
1301:
1299:0-534-13206-5
1295:
1291:
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1277:
1275:
1255:
1248:
1241:
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1200:
1196:
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1186:
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1125:
1119:
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1089:
1085:
1079:
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1057:
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1021:
1014:
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990:
986:
982:
978:
974:
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958:
954:
950:
944:
940:
936:
932:
928:
924:
920:
919:
914:
910:
909:Jiang, Jiming
897:
893:
889:
885:
881:
877:
873:
867:
863:
859:
855:
851:
850:
845:
841:
840:Jiang, Jiming
835:
833:
826:
824:
822:
819:
817:
813:
812:Eugene Dynkin
809:
805:
801:
797:
792:
788:
787:Markov chains
775:
771:
767:
761:
752:
745:
743:
723:
719:
715:
711:
707:
703:
699:
695:
691:
687:
683:
679:
678:
670:
667:(July 2000).
666:
660:
658:
656:
636:
632:
628:
624:
620:
616:
612:
608:
604:
600:
599:
591:
587:
581:
579:
559:
555:
551:
547:
543:
539:
535:
534:
526:
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518:
512:
510:
494:
493:0-8218-0668-8
490:
486:
482:
478:
474:
470:
464:
460:
455:
454:
448:
444:
440:
436:
432:
431:Robins, Sinai
429:Haga, Wayne;
425:
406:
402:
398:
394:
392:0-88385-521-6
388:
384:
377:
376:
371:
365:. p. 274
364:
363:W. H. Freeman
360:
356:
350:
348:
339:
335:
331:
327:
323:
319:
318:
313:
307:
305:
300:
286:
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278:
274:
270:
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262:
258:
254:
250:
247:According to
244:
240:
230:
227:
225:
222:
220:
217:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
185:
182:
181:
175:
173:
169:
162:
161:Kruskal count
157:
148:
146:
142:
138:
134:
130:
126:
122:
121:code breaking
118:
113:
111:
107:
103:
100:and magician
99:
95:
91:
87:
83:
79:
78:probabilistic
75:
71:
67:
63:
59:
55:
51:
50:Kruskal count
44:
37:
30:
19:
4013:Cryptography
3988:. Retrieved
3979:
3964:. Retrieved
3955:
3941:. Retrieved
3934:
3901:
3880:
3810:
3804:
3780:. Retrieved
3742:
3730:. Retrieved
3684:
3668:. Retrieved
3647:. Retrieved
3601:
3580:. Retrieved
3564:
3544:. Retrieved
3474:
3470:Bos, Herbert
3458:
3452:. Retrieved
3422:
3402:the same way
3395:
3389:. Retrieved
3376:
3358:. Retrieved
3342:
3338:
3319:. Retrieved
3307:
3297:Grime, James
3286:. Retrieved
3244:
3231:(1+10 pages)
3224:. Retrieved
3189:
3183:
3167:. Retrieved
3119:
3106:
3049:
3036:
3004:
3000:Rodgers, Tom
2996:Wolfe, David
2979:. Retrieved
2960:
2945:. Retrieved
2926:
2889:
2863:
2840:
2819:
2795:. Retrieved
2772:Plenum Press
2763:
2727:. Retrieved
2673:Fabius, Jaap
2666:
2649:. Retrieved
2583:Fabius, Jaap
2576:
2553:
2523:. Retrieved
2502:
2473:. Retrieved
2454:
2443:. Retrieved
2421:
2411:
2403:the original
2384:
2371:
2359:. Retrieved
2303:
2253:math/0110143
2239:
2206:
2193:
2157:
2153:
2130:. Retrieved
2094:
2068:
2045:
2036:
2030:
2022:
1999:
1993:Kraus (1957)
1986:
1980:
1972:
1949:
1943:Kraus (1958)
1936:
1930:
1922:
1912:. Retrieved
1898:
1894:Fulves, Karl
1880:
1877:Fulves, Karl
1871:
1862:
1856:
1847:. Retrieved
1833:
1829:Fulves, Karl
1811:
1808:Fulves, Karl
1794:
1785:
1745:
1739:. Retrieved
1721:
1709:. Retrieved
1673:
1660:
1623:cryptography
1621:, a kind of
1572:
1562:
1556:. Retrieved
1521:
1503:
1487:. Retrieved
1427:8 2 3 7 5 6
1418:
1408:E. B. Dynkin
1397:
1391:. Retrieved
1323:
1314:Jiang (2010)
1285:
1261:. Retrieved
1225:. Retrieved
1171:
1140:. Retrieved
1105:1607.03455v5
1095:
1063:. Retrieved
1038:(66 pages);
1031:. Retrieved
989:E. B. Dynkin
973:David Aldous
966:
960:. Retrieved
917:
899:. Retrieved
848:
784:
778:. Retrieved
760:
750:
729:. Retrieved
681:
675:
642:. Retrieved
602:
596:
565:. Retrieved
537:
531:
522:
496:. Retrieved
452:
424:
412:. Retrieved
374:
358:
315:
243:
194:Equifinality
172:Markov chain
165:
160:
135:, design of
117:cryptography
114:
109:
105:
73:
69:
65:
61:
57:
53:
49:
47:
43:Dynkin games
3377:dlab @ EPFL
3126:: 833–838.
3111: [
3056:: 680–683.
3041: [
2952:(4 pages);
2810:Nauka Press
2420:. Science.
2389:Basic Books
2041:(2 pages);
1805:(4 pages);
1665: [
1587:card tricks
1416:appeared in
1268:(147 pages)
736:(1+3 pages)
688:: 265–267.
609:: 437–447.
548:: 918–924.
219:Random walk
102:Karl Fulves
4002:Categories
3990:2023-09-10
3966:2023-09-05
3956:GeniiForum
3943:2023-09-05
3913:2211.10309
3892:(13 pages)
3887:card trick
3824:1812.01195
3782:2023-08-26
3732:2021-03-17
3670:2023-09-07
3654:(23 pages)
3649:2023-09-03
3587:(18 pages)
3582:2023-08-22
3551:(10 pages)
3546:2023-08-26
3454:2023-09-02
3398:card trick
3391:2023-09-04
3360:2023-08-19
3321:2023-08-19
3288:2023-08-20
3226:2023-09-02
3169:2023-09-02
2981:2023-09-03
2947:2023-09-06
2797:2023-09-03
2729:2023-09-02
2651:2023-09-02
2525:2023-09-03
2475:2023-08-19
2445:2021-12-25
2366:(12 pages)
2361:2021-12-25
2284:(22 pages)
2145:0691150028
2132:2023-08-19
2127:2007051792
2119:j.ctt7rnph
1914:2023-09-10
1849:2023-09-10
1822:(1 page);
1741:2023-08-19
1716:(10 pages)
1711:2023-08-19
1626:think tank
1615:card magic
1558:2023-09-06
1545:2011014755
1489:2023-09-01
1434:4 6 5 7 8
1412:card trick
1400:R. Durrett
1393:2023-09-01
1263:2023-08-19
1232:(17 pages)
1227:2023-08-19
1190:1509.03476
1149:(14 pages)
1142:2023-08-19
1070:(49 pages)
1065:2023-08-19
1033:2023-08-19
962:2023-09-02
901:2023-09-02
888:2010930134
796:card trick
780:2023-08-20
731:2023-08-19
649:(11 pages)
644:2023-08-19
567:2023-08-19
498:2023-08-19
414:2023-08-19
295:References
151:Card trick
90:card trick
3851:1099-4300
3769:1654-790X
3525:0302-9743
3507:1611-3349
3485:(DIMVA).
3464:(2 pages)
3441:1027-488X
3369:West, Bob
3326:(8 pages)
3258:0812.0789
3216:117632058
3208:1551-3440
3174:(6 pages)
3156:121242696
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