# such of sum of any two adjacent numbers is equal to the sum of the opposite numbers

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

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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