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Sam stacks cans in his shop in triangular stacks, one can deep, (see the problem Cat Food ).
Jennifer from the Mount School York warned Sam that stacks of cans like this are very likely to fall over. It's better to stack in a pyramid: for example. $P_4$ has $16$ on the base, then $9$ then $4$ and finally $1$.
These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...