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 Adjacent Square Sum II (Posted on 2013-06-10)
In the six rows of numbers below, each of the pairs adds up to 25. Now 25 happens to be a perfect square.

Fill in the blanks with a third number (a different number in each row) so that the sums of any two numbers on any row is a perfect square.
```+---+---+---+
| 1 |24 |   |
+---+---+---+
| 2 |23 |   |
+---+---+---+
| 3 |22 |   |
+---+---+---+
| 4 |21 |   |
+---+---+---+
| 5 |20 |   |
+---+---+---+
| 6 |19 |   |
+---+---+---+```

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 The algebra | Comment 3 of 5 |
Inspection of Charlie's solution leads to a nice pattern.

The numbers in the chart are n and (25-n)

If we add (9-n)(16-n)=n-25n+144 to each we get

n²-24n+144 = (n-12)² and n²-26n+169 = (n-13)²

The numbers are based on the 5,12,13 pythagorean triple.

Edited on June 10, 2013, 2:21 pm
 Posted by Jer on 2013-06-10 14:15:21

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