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At first glance it seems that the shortest distance between A and B is the straight way along the sides of the box, i.e. 1 unit up, 30 units along the top side of the box and then 11 units down the opposite side - 42 units in total. But as it was stated in the hint the shortest distance between A and B is less than 42.

To find the shortest distance out it is useful to unfold some sides of the box into a 2D model. If to unfold them as shown in the lower right corner of the illustration, we get a right triangle where the hypotenuse AB is the distance between the two spots. It equals square root of (AC2 + BC2). AC is 32 units long (1 + 30 + 1) and BC is 24 units long (6 + 12 + 6). Thus the distance AB equals square root (322 + 242) = square root of 1600 or 40.!

Last Updated: July 9, 2008  |  Posted: April 5, 2004
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