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  
++++
Inspection of Charlie's solution leads to a nice pattern.
The numbers in the chart are n and (25n)
If we add (9n)(16n)=n25n+144 to each we get
n²24n+144 = (n12)² and n²26n+169 = (n13)²
The numbers are based on the 5,12,13 pythagorean triple.
Edited on June 10, 2013, 2:21 pm

Posted by Jer
on 20130610 14:15:21 