Question 5
Ten rectangles form a pyramid. Each rectangle is filled with a positive whole number following a certain rule. The bottom numbers 3, 2, 1, 5 produce the displayed pyramid and the top number 120.
(a) What is the rule for filling the rectangles?
(b) Using that rule, what is the top number when the bottom numbers are 1, 2, 1, 3 in this order?
(c) The same rule gives 2160 at the top. Find all possible ordered bottom rows if the number 1 is not used. The order 3,2,2,4 is considered different from 4,2,2,3.
(a) What is the rule for filling the rectangles?
(b) Using that rule, what is the top number when the bottom numbers are 1, 2, 1, 3 in this order?
(c) The same rule gives 2160 at the top. Find all possible ordered bottom rows if the number 1 is not used. The order 3,2,2,4 is considered different from 4,2,2,3.