UKMT - Grey Kangaroo - 2023 - 6

6

Anna has five circular discs, each of a different size. She decides to build a tower using three of her discs so that each disc in her tower is smaller than the disc below it. How many different towers could Anna construct?

A 5 B 6 C 8 D 10 E 15

Answer

SOLUTIOn

Let the discs be numbered 1, 2, 3, 4 and 5 in increasing order of size. The possible towers using three discs that Anna can build are, with the first number on top and then going down the tower, 123, 124, 125, 134, 135, 145, 234, 235, 245 and 345. Therefore she can build 10 different towers.

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