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#1 2008-09-29 23:30:18
- tony123
- Member
- Registered: 2007-08-03
- Posts: 230
5 by 5 array
In the 5 by 5 array, the numbers in every row, every column and both diagonals
form arithmetic progressions.
You are given that
. Find the sum of the 25numbers in the array.
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#2 2008-09-30 04:20:37
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: 5 by 5 array
Let
The fourth column forms AP
The fifth row forms AP
And the diagonals form AP
Hence the array is
The sum of the entries of each row is 5 times the number in the middle column, and the sum of the numbers in the middle column is 5 times 24. Hence the sum of all the entries in the array is 25 × 24 = 600.
Last edited by JaneFairfax (2008-09-30 04:30:14)
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