## THE STONEMASON'S PROBLEM.

(

Money Puzzles)

A stonemason once had a large number of cubic blocks of stone in his

yard, all of exactly the same size. He had some very fanciful little

ways, and one of his queer notions was to keep these blocks piled in

cubical heaps, no two heaps containing the same number of blocks. He had

discovered for himself (a fact that is well known to mathematicians)

that if he took all the blocks contained in any number of heaps in

regular order, beginning with the single cube, he could always arrange

those on the ground so as to form a perfect square. This will be clear

to the reader, because one block is a square, 1 + 8 = 9 is a square, 1 +

8 + 27 = 36 is a square, 1 + 8 + 27 + 64 = 100 is a square, and so on.

In fact, the sum of any number of consecutive cubes, beginning always

with 1, is in every case a square number.

One day a gentleman entered the mason's yard and offered him a certain

price if he would supply him with a consecutive number of these cubical

heaps which should contain altogether a number of blocks that could be

laid out to form a square, but the buyer insisted on more than three

heaps and _declined to take the single block_ because it contained a

flaw. What was the smallest possible number of blocks of stone that the

mason had to supply?

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THE SULTAN'S ARMY.
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THE BANKER'S PUZZLE.