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On a ruckle problem in discrete games of ambush

✍ Scribed by A.Y. Garnaev

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
88 KB
Volume
44
Category
Article
ISSN
0894-069X

No coin nor oath required. For personal study only.

✦ Synopsis

The following zero-sum game is considered. Red chooses in integer interval [1, n] two integer intervals consisting of k and m points where k / m Γ΅ n, and Blue chooses an integer point in [1, n]. The payoff to Red equals 1 if the point chosen by Blue is at least in one of the intervals chosen by Red, and 0 otherwise. This work complements the results obtained by Ruckle, Baston and Bostock, and Lee.

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The game of 'Mousetrap, a problem in permutations, first introduced by Arthur Cayley in 1857 and independently addressed by Cayley and Adolph Steen in 1878, has been largely unexamined since. The game involves permutations of \(n\) cards numbered consecutively from 1 to \(n\). The cards are laid out