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Post History
There are $100$ marbles in a bucket. Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first. At each turn the player can choose to remove eith...
#3: Post edited
by
will.octagon.gibson
·
2026-09-18T06:03:19Z (about 9 hours ago)
Added the strategy-game tag
#2: Post edited
by
will.octagon.gibson
·
2026-05-23T15:14:00Z (4 months ago)
Added a link to a related puzzle
- There are $100$ marbles in a bucket.
- Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first.
- At each turn the player can choose to remove either $1, \ 2, \ 3 \ or \ 4$ 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?
- There are $100$ marbles in a bucket.
- Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first.
- At each turn the player can choose to remove either $1, \ 2, \ 3 \ or \ 4$ 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/296186
#1: Initial revision
by
will.octagon.gibson
·
2026-05-21T22:34:39Z (4 months ago)
Alpha and Beta play a game with marbles
There are $100$ marbles in a bucket. Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first. At each turn the player can choose to remove either $1, \ 2, \ 3 \ or \ 4$ 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?