Round Table Coin Game
Here is an old puzzle that I have used in my classes for years.
Puzzle. Two people take turns placing quarters on a round table so that the quarters fit on the table and no two quarters overlap. The person who can’t move loses. Who has a winning strategy?
It is easy to see that the first player always wins by using the symmetry of the table. On the first move, the first player puts the first coin directly in the center of the table. For each subsequent move, the first player places a coin in the spot that is centrally symmetric to where the coin was placed on the previous move.
This year, something unusual happened. It seems I have a couple of true mathematicians among my STEP students. They added the following detail.
The first player wins, except when the table is smaller than the quarter.
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Ivan:
The unjustified assumption is the mother of all … you know. This is what your current students found: the assumption that the table is bigger that the coin was unjustified.
What about the referendum puzzle? Is the assumption that all citizens answer all questions is justified? Is the assumption that they may answer with NO is justified? We remember how in the communist countries all was decided in advance and the elections/referendums were just rubber-stamping.
Let’s take the time machine and return to my comment on your Identical Triplets Puzzle: the assumption that the heights and looks of the identical triplets are the same is unjustified.
1 October 2026, 12:09 amFreedom Calcs:
The boundary case sharpens the statement nicely. If the table has exactly the same diameter as the coin, the first move already fills it, so the usual conclusion still holds. Asking students to separate the smaller-than, equal-to, and larger-than cases seems a good way to turn that objection into a more precise theorem rather than just a gotcha.
20 October 2026, 2:03 am