Dissections – the Greek cross

The Greek cross consists of 5 squares joined in the shape of a cross.

1) Greek cross – 4 equal parts*
Greek cross 4 equal parts exercise
The figure above shows a strangely formed meadow between a brook and mountains. There are 4 wells in the area. The farmer died and stipulated in his will that his land would be distrubuted equally among his 4 sons; all 4 lots would have the same area and shape and contain exactly 1 well.

How was the land divided among the 4 sons?

2) The hindu problem
Dudeney Greek cross dissection problem
The greek cross as shown in the illustration to the left, is composed of 5 equal sized squares. Cut the cross into five pieces to form a square. There are 2 solutions. According to British puzzle master Henry Dudeney, the problem is over 3000 years old.

3) How many straight cuts?
Henry Dudeney next comes up with the problem:
How many cuts do you need to divide the Greek cross into 4 pieces, so that with these pieces you can form a square?

4) The Red CRoss Lassie
American puzzle master Sam Loyd recounts the following problem:
Red Cross Lassie
In the whole realm of puzzledom, and geometry included, there is nothing so fascinating and eminanetly scientific as the series of problems pertaining to the form of the Greek cross and its peculiar relations to the square, parallelograms and other symmmetrical shapes.
As differing from the well known mathematical problem of converting the cross into a square by the fewest possible number of cuts, attention is called to the following pretty feat of chaninging one cross into two.
It appears that one of our wounded boys in blue who was returning home after being nursed back to life by a faithful Red Cross lassie, begged the red cross from her arm as a keepsake; but she, in true sweetheart style, took her scissors and by a few deft clips, cut the red cross into several pieces, which could be fitted together perfectly so as to make two crosses of similar vsize. It is a simple but beautiful trick, and the satisfaction of guessing it will be as great as if you should win a prize.

You can check your solution here for no 1, here for no 2 and here for no 3, and here for no 4

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?


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