query: Nim-Like Game: Subtracting powers of 2 from 1000.
positive_passages.docid: 141703
positive_passages.text: Is there any winning strategy? 2015 and Game with marbles!!!
negative_passages.docid: 135124
negative_passages.text: Calculating the expected payoff in a 2-finger morra game
negative_passages.docid: 38380
negative_passages.text: An infinite Penney's game.
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 106955
negative_passages.text: Algorithm for Determining Tic Tac Toe Game Over
negative_passages.docid: 136037
negative_passages.text: ${n\choose 2} - {k\choose 2} = {n-k\choose 2} +k(n-k)$ Marked box or unmarked box
negative_passages.docid: 10724
negative_passages.text: Case of the 'mice problem' for $n=3$
negative_passages.docid: 68507
negative_passages.text: Random number generation and probability
negative_passages.docid: 35368
negative_passages.text: Is it possible to play the Tower of Hanoi with fewer than $2^n-1$ moves?
negative_passages.docid: 47697
negative_passages.text: Russell's paradox: a set cannot contain its own powerset
negative_passages.docid: 139826
negative_passages.text: arbitrary large finite sums of an uncountable set.
negative_passages.docid: 129693
negative_passages.text: An interesting problem with "decomposing" natural numbers.
negative_passages.docid: 68308
negative_passages.text: A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$
negative_passages.docid: 38074
negative_passages.text: Winning strategies in multidimensional tic-tac-toe
negative_passages.docid: 70677
negative_passages.text: Finite Sum of Power?
negative_passages.docid: 17097
negative_passages.text: Number of moves necessary to solve Rubik's cube by pure chance
negative_passages.docid: 104176
negative_passages.text: $15x\equiv 20 \pmod{88}$ Euclid's algorithm