Mathematics
Pink Kangaroo
2023
3

3

A wooden fence consists of a series of vertical planks, each joined to the next vertical plank by four horizontal planks. The first and last planks in the fence are vertical. Which of the following could be the total number of planks in the fence?

A 96 B 97 C 98 D 99 E 100

Answer

A

SOLUTIOn

The first panel of this fence consists of 6 planks (2 vertical and 4 horizontal); every additional panel consists of 5 planks (another vertical and 4 horizontal). So the number must be some number of the form 5푥 + 1 for 푥 ≥ 1. The only such number listed is 96.

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