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1-2-3-4 Square (Posted on 2016-08-12) Difficulty: 3 of 5
A square has an area of 10 cm^2. Two straight lines are drawn across the square dividing it into four areas of 1 cm^2, 2 cm^2, 3 cm^2, and 4 cm^2.

Where can those lines be drawn?

No Solution Yet Submitted by Brian Smith    
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More generally | Comment 2 of 3 |
If the 1 and the 4 are contiguous, then any line going through the center will dividing the square into a 5 and 5.  Then a 2nd line can always be drawn (not through the center) diving one area into a 4 and 1 and the other into a 2 and a 3.   

If the 1 and 4 are not contiguous, then neither line goes through the center.  Still lots of ways to do it.

In no case are both lines parallel to the sides of the square.

Edited on August 12, 2016, 10:06 am
  Posted by Steve Herman on 2016-08-12 10:01:14

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