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And counting (Posted on 2019-02-28) Difficulty: 3 of 5
a + b + c = 3
a2 + b2 + c2 < 10
a3 + b3 + c3 = 15
a4 + b4 + c4 = 35
a5 + b5 + c5 = m

Find m.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Wolfram Alpha's solution | Comment 2 of 4 |
Working with Wolfram Alpha again, requiring an upgrade to Pro Premium this time, leads to the set of values for x, y and z (using x, y and z instead of a, b and c) (obviously order doesn't matter) being 1, 1-sqrt(2) and 1+sqrt(2). Wolfram doesn't specifically tie the solutions for x, y and z together, but it seems the first solution given for x goes with the first solution for y, etc., even though all the x solutions are listed first, then all the y solutions, then all the z solutions.

In any event m = 83. And BTW the total of squares is 7, which is indeed under 10.

  Posted by Charlie on 2019-02-28 19:43:36
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