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Adjacent Square Sum II (Posted on 2013-06-10) Difficulty: 2 of 5
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    
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Solution re: No Subject few remarks+ challenges Comment 5 of 5 |
(In reply to No Subject by Charlie)

..."Also it can be extended two more rows:...


Why two? It can be extended indefinitely  in both directions, as long as the triplet of integers is  t, 25-t, (12-t)^2-t.

e.g.    t=9:   9,16,-5;     t=26: 26,-1,170;   t=100: 100,-75; 7644.
Extra challenges(everybody, not just Ch):
1.Derive the the formula (in bold ) for (a,b,c)- a+b=25
2,Derive a general  formula  for (a,b,c), any two add up to 
a square, given  a+b=(odd integer)^2.
BTW, Ch - 2nd row in the bottom table is erroneous (typo),
please edit for history sake,

  Posted by Ady TZIDON on 2013-06-10 16:58:08
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