MathDB

Soma has a tower of

63

bricks , consisting of

6

levels. On the

k

-th level from the top, there are

2k-1

bricks (where

k = 1, 2, 3, 4, 5, 6

), and every brick which is not on the lowest level lies on precisely

2

smaller bricks (which lie one level below) - see the figure. Soma takes away

7

bricks from the tower, one by one. He can only remove a brick if there is no brick lying on it. In how many ways can he do this, if the order of removals is considered as well?
https://cdn.artofproblemsolving.com/attachments/b/6/4b0ce36df21fba89708dd5897c43a077d86b5e.png

Problem Statement