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Sunday, March 21, 2010

Exercise - continued

A positive integer is written on each face of a cube. Each vertex is then assigned the product of the numbers written on the three faces intersecting the vertex. The sum of the numbers assigned to all the vertices is equal to 1001. Find the sum of the numbers written on the faces of the cube.

I found this exercise in a problem book for Number Theory. The type of book which is used for training young students who participate in Math Contests. I spend a few hours on this problem today and managed to solve it in my third attempt or so. The risk of problems of a more than elementary nature is that they may cost a lot of time. Although I managed to solve it I can't say I did it in a standard way, using some cookbook recipe. All sorts of ideas kept coming up. The gateway to the solution was a link I noticed between this problem and the Instant Insanity problem.

I'll post the answer if someone requests for it, of course. Although I more or less gave it away above.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)