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# cross sum

2 replies to this topic

### #1 brhan

brhan

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Posted 29 September 2007 - 01:06 PM

Put the numbers from 2 to 8 (without repeating) in each circle of the following diagram such that sum of the three numbers placed in a straight line (vertical, horizontal or diagonal) is 15.

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### #2 Benson

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Posted 29 September 2007 - 04:51 PM

Define:
1. x as the top of the trangle
2. y as the sum of a straight line

Then,
2x + 35 = 3y (from the x down to three straight line)
35 - x = 2y (from the horizontal two straight line)
=> x = 5, y = 15

So, the remains is the sum of 10. that is, {2,8}, {3,7}, {4,6}. Fill in and make sure the straight line is 15.

For example,
5
276
8 3 4
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### #3 brhan

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Posted 01 October 2007 - 10:52 AM

Good work from Benson.

The difficulty might be what number to place on the top circle. Let say X.
Then, since the sum of the numbers from 2 to 8 is 35,
==> X + 2*15 = 35 (For the two horizontal row sums).
==> X = 5.

Then as Benson said, pairing remaining numbers such that their sum is 10 -- 2 & 8; 3 & 7 and 4 & 6.
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