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4 numbers make 5 squares (Posted on 2016-06-30) Difficulty: 3 of 5
Find four whole numbers such that:

each pairwise sum is a perfect square and
the sum of all four is a perfect square.

No Solution Yet Submitted by Jer    
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A (bad?) guess | Comment 4 of 10 |
There is a problem with the formulation of this puzzle, because the title says "4 numbers make 5 squares" and the wording inside says:
"four numbers such that each pairwise sum is a perfect square".

But if I have four number there are six pairwairs (XY, XW, XZ, YW, YZ, WZ). If also the sum is a perfect square then we will have seven squares in total and not five. 

My (perhaps-probably) bad guess is that Charlie is not finding solution because he is searching for 7 squares, while the intended solution is for 5 squares (for ex: XY, XW, XZ, WZ, X+Y+W+Z). 

If my hypothesis is wrong I apologize...

Changing theme I can find a lot of XY, XW, XZ, WZ, squares, but is quite more difficult to place the other three. F. ex. 

X=1440 Y=324 W=3888 Z=7776 makes: 

Edited on July 1, 2016, 10:20 am
  Posted by armando on 2016-07-01 09:33:00

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