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pro vyhledávání: '"00A08"'
Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations and provide
Externí odkaz:
http://arxiv.org/abs/2411.10207
Autor:
Inosov, Dmytro S., Vlasák, Emil
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in the form
Externí odkaz:
http://arxiv.org/abs/2410.21427
Autor:
Byrapuram, Nikhil, Ge, Adam, Ge, Selena, Khovanova, Tanya, Lee, Sylvia Zia, Mandal, Rajarshi, Redwine, Gordon, Samanta, Soham, Wu, Daniel, Xu, Danyang, Zhao, Ray
The following magic trick is at the center of this paper. While the audience writes the first ten terms of a Fibonacci-like sequence (the sequence following the same recursion as the Fibonacci sequence), the magician calculates the sum of these ten t
Externí odkaz:
http://arxiv.org/abs/2409.01296
Autor:
Gladkov, Nikita, Pak, Igor
We consider a probabilistic version of the depth-first search on mazes with two exits, and show that this algorithm has equal probability of finding either exit. The proof is combinatorial and uses an explicit involution.
Comment: This paper is
Comment: This paper is
Externí odkaz:
http://arxiv.org/abs/2408.00978
Autor:
Johnson, Inga, Roldan, Erika
The 30 MacMahon colored cubes have each face painted with one of six colors and every color appears on at least one face. One puzzle involving these cubes is to create a $2\times2\times2$ model with eight distinct MacMahon cubes to recreate a larger
Externí odkaz:
http://arxiv.org/abs/2407.13208
Autor:
Nishiyama, Yutaka
Hermann discovered the grid illusion in 1870, but its cause has remained a mystery for more than 150 years. In 1960, Baumgartner proposed a hypothesis for the illusion based on neural receptive fields, but Geier presented a counterexample in 2008. In
Externí odkaz:
http://arxiv.org/abs/2408.00782
Autor:
Richeson, Benjamin, Richeson, David
Left, Center, Right is a popular dice game. We analyze the game using Markov chain and Monte Carlo methods. We compute the expected game length for two to eight players and determine the probability of winning for each player in the game. We discuss
Externí odkaz:
http://arxiv.org/abs/2407.05069
Autor:
Chen, Aria, Cummins, Tyler, De Francesco, Rishi, Greene, Jate, Khovanova, Tanya, Meng, Alexander, Parida, Tanish, Pulugurtha, Anirudh, Swaroop, Anand, Tsui, Samuel
Fitch Cheney's 5-card trick was introduced in 1950. In 2013, Mulcahy invented a 4-card trick in which the cards are allowed to be displayed face down. We suggest our own invention: a 3-card trick in which the cards can be face down and also allowed t
Externí odkaz:
http://arxiv.org/abs/2405.21007
Autor:
Byrapuram, Nikhil, Ge, Adam, Ge, Selena, Khovanova, Tanya, Lee, Sylvia Zia, Mandal, Rajarshi, Redwine, Gordon, Samanta, Soham, Wu, Daniel, Xu, Danyang, Zhao, Ray
In 2013, Conway and Ryba wrote a fascinating paper called Fibonometry. The paper, as one might guess, is about the connection between Fibonacci numbers and trigonometry. We were fascinated by this paper and looked at how we could generalize it. We di
Externí odkaz:
http://arxiv.org/abs/2405.13054
Autor:
Malinovsky, Yaakov, Sonin, Isaac M.
We present a variation of the water puzzle, which is related to a simple model of marginal utility. The problem has an exciting solution and can be extended in several directions.
Externí odkaz:
http://arxiv.org/abs/2404.10015