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Give the numbers 1 to 10 on the edges of the diametric chords for the image given below such that such of sum of any two adjacent numbers is equal to the sum of the opposite numbers

image divided into 10 parts

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1 Answer 1

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Going clockwise

$$10, 1, 4, 5, 8, 9, 2, 3, 6, 7$$

is a solution.

The pairs to compare are:

$$10 + 1 = 9 + 2 \\ 1 + 4 = 2 + 3 \\ 4 + 5 = 3 + 6 \\ 5 + 8 = 6 + 7 \\ 8 + 9 = 7 + 10$$

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For how I actually got that, I started with the guess that (1,10) and (2,9) would be pairs, and worked my way clockwise, going up. –  Dennis Meng Nov 7 '13 at 18:43
    
Is there any logic you have used –  sai kiran grandhi Nov 7 '13 at 18:46
    
Well, as an example, while I was working clockwise, I knew that 1 and 2 would be in another set of pairs, where 1's partner is once again one higher than 2's partner (and similar reasoning while working around the circle). Why I chose 3 and 4 next mostly amounts to intuition and a bit of luck. –  Dennis Meng Nov 7 '13 at 18:48
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