Sam displays cans in 3 triangular stacks. With the same number he
could make one large triangular stack or stack them all in a square
based pyramid. How many cans are there how were they arranged?
Here is a collection of puzzles about Sam's shop sent in by club
members. Perhaps you can make up more puzzles, find formulas or
find general methods.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
2 x 1 = 2,
3 x 2 x 1 = 6,
4 x 3 x 2 x 1 = 24,
5 x 4 x 3 x 2 x 1 = 120,
6 x 5 x 4 x 3 x 2 x 1 = 720....
The 3 digit numbers less than 500 which are sums of consecutive
144, 150, 152 and 153.
The only one of these numbers which satisfies the condition that
it is equal to the sum of the cubes of its digits is 153 because
153 = 1 + 125 + 27 so this must be the forgotten number. The
information about triangular numbers was not needed but it is
easily checked that 153 is a triangular number.
An excellent solution was recieved from Ben
from Methwold High School.