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Cutting the Card (Posted on 2009-09-16) Difficulty: 2 of 5
Take a card that is 6 cm by 12 cm, and mark the center point.

Then draw four straight line segments, each from the center point to the perimeter, and each an integral number of centimeters long, so that if you wish to cut off an area of any integral multiple of 6 cm2, you need only cut along two of these lines. Of course cutting off a multiple of 6 cm2 will also leave a multiple of 6 cm2.

What are the lengths of the four segments and how can they be arranged around the center?

See The Solution Submitted by Charlie    
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Some Thoughts Congratulations (and correction) Comment 3 of 3 |
Congratulations to Stephanie and Daniel, who came up with two different solutions.  

Stephanie has areas of 6,36,12,18 (going clockwise).

Daniel made one little mistake.  His line W needs to be drawn to (6,2) in order to be integral, which I'm sure is what was intended. After this line is redrawn, then his areas are 6,12,24 and 30 (going clockwise)





  Posted by Steve Herman on 2009-09-20 11:13:20
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