Friday, 25 November 2011

Puzzle -26


H
G
A
B
O
C
D
E
F

A,B,C,D,E,F,G,H,O are distinct single digit non-zero positive integers placed as shown in the above diagram. Given that, sum of numbers placed north of ‘O’ = sum of numbers placed south of ‘O’ = sum of numbers placed east of ‘O’ = sum of numbers placed west of ‘O’. Then find all the possible values of ’O’?
(1)1,2,3                       (2)1,3,5                       (3)1,5,9                       (4)2,4,6                       (5)1,3,9
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4 comments:

  1. Pradeep Sadanapalli26 November 2011 at 01:11

    Option 3: 1,5,9 going symmetrically

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  2. MathByVemuri26 November 2011 at 14:26

    Symmetry of 1,5,9 - it is a good idea Pradeep. Given the symmetry of the problem, the answer should by symmetric.

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  3. Anonymous2 November 2012 at 16:35

    The sum 1 + ... + 9 = 45. By removing the value of 'O' we are left with a sum that has to be a multiple of 4. The possible options are: 44, 40, 36. Subtracting these from 45 we get 1, 5, 9.

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    Replies
    1. MathByVemuri2 November 2012 at 18:00

      I think this is the best logical solution. kudos..

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