UCD Openday 1999
Mathematics Problem
You must follow the rules.
UCD Openday 1999 Mathematics Problem
eleven steps with five stones
Can Sisyphus raise a rock to the very top?
A pyramid consists of 1001 steps. Initially 500 rocks are placed,
one on each of the lowest 500 steps, while the remaining steps
are left empty.Sisyphus and the Demon take turns, Sisyphus
moving a rock up and the Demon moving a rock down.
In each move
Sisyphus must choose one rock and move it to the lowest unoccupied
step above itself. In each move the Demon must choose a rock
immediately above an unoccupied step and move that rock down to that
step. Sisyphus takes the first move but the Demon plays with skill
and cunning.
Can Sisyphus raise a rock to the very top step?
If he can, explain how?
If he can not, explain why not?
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Revised 22 Mar 1999.