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The Haberdasher's Puzzle

Many attempts were made to induce the Haberdasher, who was of the party, to propound a puzzle of some kind, but for a long time without success. 
At last, at one of the Pilgrims' stopping-places, he said that he would show them something that would "put their brains into a twist like unto a bell-rope." 
As a matter of fact, he was really playing off a practical joke on the company, for he was quite ignorant of any answer to the puzzle that he set them. 
He produced a piece of cloth in the shape of a perfect equilateral triangle, as shown in the illustration, and said, "Be there any among ye full wise in the true cutting of cloth?
I trow not. 
Every man to his trade, and the scholar may learn from the varlet and the wise man from the fool. 
Show me, then, if ye can, in what manner this piece of cloth may be cut into four several pieces that may be put together to make a perfect square."

Now some of the more learned of the company found a way of doing it in five pieces, but not in four. 
But when they pressed the Haberdasher for the correct answer he was forced to admit, after much beating about the bush, that he knew no way of doing it in any number of pieces. 
"By Saint Francis," saith he, "any knave can make a riddle methinks, but it is for them that may to rede it aright." 
For this he narrowly escaped a sound beating. 
But the curious point of the puzzle is that I have found that the feat may really be performed in so few as four pieces, and without turning over any piece when placing them together. 
The method of doing this is subtle, but I think the reader will find the problem a most interesting one.

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