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Age 11 to 14 Short Challenge Level:

Pegs numbered $1$ to $50$ are placed in order in a line, with number $1$ on the left.

They are then knocked over, one at a time, following these rules:
  • Starting with the first standing peg on the left, alternate pegs are knocked down, until the end of the row is reached.
  • Each time the end of the row is reached, repeat the previous rule.
What is the number of the last peg to be knocked down?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.