10 May 2013

Prize Maths Quiz: Number Puzzle on a Truncated Cube (PMQ18)

Imagine a cube with a positive integer written on each of its six faces. Now imagine cutting the vertices of this cube; the resulting solid is known as a truncated cube, or truncated hexahedron, and is shown in the image. The six original squares are now octagons, but the integers remain unchanged, and the eight vertices have become triangles. Let the number on each triangular face be the product of the three numbers written on the octagons that share an edge with it.

The sum of the numbers on all the triangles is equal to 6006. Find the smallest possible sum of the original six numbers written on the faces of the cube.

[This question has been adapted from 104 Number Theory Problems: From the Training of the USA IMO Team]

You may discuss the question below, but no full answers, please, until the competition has closed!

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How to Enter

Send your complete solution by email to pmq18feynman@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ18 competition closes on MONDAY 13 May at 23:59 GMT - one extra weekday from now on.

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
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