1yes, your approach is right sir, i too got the same answer
thanks for the proof
Is it possible to number the 8 vertices of a cube from 1 to 8 in such a way that the value of the sum on every edge is different?
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3 Answers
341This is more of a logic puzzle.
Its not possible. Because:
The numbers that can appear on the edges range from 3 to 15, thats 13 numbers. So if all the numbers are to be distinct we have to drop a number.
We can, in fact, find that number. No matter how the vertices are numbered, the sum of the numbers on the edges is always 108 (why?). Since 3+4+5+...+15 = 117, we have to drop 9.
What this means is that 3,4,5 and 6 all have to appear on the edges. This means that 1 is connected to 2,3 and 4 and further 2 and 4 lie on different edges. But this means the number 6 cannot appear as we cannot pair 1 and 5 too as all three 'valencies' of 1 are taken up and (1,5) and (2,4) are the only pairings that can produce a 6
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