Knockdown
Weekly Problem 51 - 2016
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?
Age
11 to 14
Challenge level
Problem
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.
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 32
First round:
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Second round:
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Third round:
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Fourth round: Only multiples of 16 will be left
Fifth round: Only multiples of 32 will be left.
32 is the only multiple of 32 under 50, so 32 is the last number left.