Find four whole numbers such that:
each pairwise sum is a perfect square and
the sum of all four is a perfect square.
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 (perhapsprobably) 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...
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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:
X+Y=42^2
W+Z=108^2
Z+X=96^2
Z+Y=90^2
Edited on July 1, 2016, 10:20 am

Posted by armando
on 20160701 09:33:00 