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Cans in a cooler (Posted on 2013-02-11) Difficulty: 3 of 5
Lay 14 identical soda cans (lettered A-N)in a rectangular cooler with the following specifications:

The cooler is more than wide enough to lay down 4 cans but not wide enough for 5. Cans A, B, C, D lie next to each other to form the first layer with A and D against the corners. B and C are free to move a bit.

The next layer is E in the groove between A and B, F in the groove between B and C, G in the groove between C and D.

The next layer is H along the side of the cooler above E, I and J in the next two grooves, K along the other side above G.

The final layer L, M, N along the grooves of the previous layer.

Prove: no matter where B and C are at the bottom, the cans L, M, N are equally spaced and in a straight line.

  Submitted by Jer    
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Solution: (Hide)
It's easy if you follow the angles formed by the centers of the cans up.

Call angles AEB = x, BFC = y, CGD = z
The angles LIM and MJN end up both the same (x+z)/2 which shows they are equidistant.
The three angles at M are 90-(x+z)/4, (x+z)/2, 90-(x+z)/4 which add to 180 which shows the cans are in a line.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
An interactive Wolfram DemonstrationJer2016-08-04 22:10:34
re: A picture - some thoughtsbrianjn2013-02-14 02:57:15
A pictureJer2013-02-13 13:01:31
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