Try This Month’s Challenge!

Welcome to our “Ponder This” monthly puzzles. You are cordially invited to match wits with some of the best minds in IBM Research. Forge ahead and ponder this month’s problem!

Ponder This Challenge:

32 pebbles are placed on the six edges of a tetrahedron, as shown in the following figure.


Two players are playing a game. Each player, on her turn, can take as many pebbles as she chooses, but a minimum of one pebble must be taken each turn, and all the pebbles taken must be on the same face. If you cannot play (i.e., if all the pebbles are taken) – you lose.

What are the winning moves, for the first player, in this situation?

For example, if the first player plays 0,0,3,0,8,13 i.e., taking the whole northeast face, leaving the tetrahedron as 1,2,0,5,0,0; then the second player can win by playing 0,1,0,4,0,0 on the bottom face which leaves 1,1,0,1,0,0; and for every possible move of the first player, the second player can immediately win.

Please supply your answer as a list of lines, each line is a possible move.


IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission. Send your submission to the webmaster.

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