 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  4 numbers make 5 squares (Posted on 2016-06-30) 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 No Rating Comments: ( Back to comment list | You must be logged in to post comments.) 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:
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 2016-07-01 09:33:00 Please log in:

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