Enigma 1420: a² + b² + c²
17 June 2013
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From New Scientist #2580, 2nd December 2006
This puzzle is concerned with the equation a² + b² + c² = d² + e² + f², where a, b, c, d, e, and f are different integers between 1 and 9.
I found a solution to that equation. I then altered just one of the integers on each side of that solution to create a second solution. I then altered just one of the integers on each side of the second solution to create a third solution. I then altered just one of the numbers on each side of the third solution to create a fourth solution. All four solutions were different.
If the fourth solution produced a larger sum than the first solution, what was the value of (a² + b² + c²) in each of the four solutions in order?