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There are $146$ marbles in a bucket. Delta and Epsilon play a game in which they take turns removing marbles from the bucket with Delta going first. At each turn the player can choose to remove e...
#1: Initial revision
by
will.octagon.gibson
·
2026-05-23T02:59:31Z (4 months ago)
Delta and Epsilon play a game with marbles
There are $146$ marbles in a bucket. Delta and Epsilon play a game in which they take turns removing marbles from the bucket with Delta going first. At each turn the player can choose to remove either $1, \ 4 \ or \ 6$ marbles from the bucket. Whoever empties the bucket wins the game. Could either player have a winning strategy that would ensure that they win no matter how their opponent plays? --- **See also:** I posted a related puzzle here: https://proposals.codidact.com/posts/296179 --- **Attribution:** A puzzle like this was used in the Hanoi team training for the International Math Tournament of the Towns in approximately 2016.