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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.

13 votes
4 answers
3k views

Mathematical model for Hanoi Towers

The strategy for the Hanoi Tower puzzle is quite simple. It is based on parity only. In an $n$-pieces puzzle, $2^n-1$ moves are sufficient to carry the whole pile from one pole to another one. … My question is Is there any mathematical (algebraic, logical, ...) structure associated with the Hanoi Tower puzzle? …
Denis Serre's user avatar
  • 52.3k
54 votes
3 answers
7k views

cube + cube + cube = cube

Several comments ask for a reference for the $8$-pieces puzzle, mentioned at first in the question. Actually, $8$ was a mistake, as the solution I know consists of $9$ pieces. … Yet it is not very informative, so let me give you additional information (I manipulated the puzzle a couple weeks ago). There is a $2$-cube (middle) and a $3$-cube (right). …
Denis Serre's user avatar
  • 52.3k
29 votes
6 answers
7k views

Integers in a triangle, and differences

I read about the following puzzle thirty-five years ago or so, and I still do not know the answer. …
Denis Serre's user avatar
  • 52.3k
26 votes
3 answers
3k views

What is this subgroup of $\mathfrak S_{12}$?

On some occasion I was gifted a calendar. It displays a math quizz every day of the year. Not really exciting in general, but at least one of them let me raise a group-theoretic question. The quizz: …
Denis Serre's user avatar
  • 52.3k