A Hand Calculation — NO COMPUTERS ALLOWED!

Well, it’s been a while since my last post.  I’ve been busy.  Here is something that will keep you busy as well.  There is only one rule.  You must solve this problem with paper and pencil only — No Computers Allowed.  It is easily solved by a computer, but where’s the fun?  Where’s the understanding?

To the best of my memory, this problem first came to my attention in the 1960’s.  That was before we had personal computers.  Back then, it had to be solved by hand (and mind).  I gave this problem to a colleague a few years ago with the same admonition to not use a computer.  He was really proud of himself for solving it with his computer.  Good computer, bad memory.

Anyway, as I recall, I found this in a copy of Aviation Week.  If my memory is wrong on this, my apologies.  I do not recall if the problem listed its author.  Here goes:

There are three rectangles of the same area.  The area is a positive whole number.  (no hidden  tricks)  The sides are as follows:

X by (X – 278), Y by (Y – 96), and Z by (Z – 542)

X, Y, and Z are also positive whole numbers.

What is the area?

I assure you, there is only one correct answer.  And you can fit the solution on one side of one sheet of 8X10 paper if you don’t write too big.  You don’t have to write all that small either.  However, use as much paper as you want.

I’ll post my solution in late June.  I have an old handwritten version that I can scan.  I wrote fairly big, so it took three pages.  However, I could fit it on one page if pressed only slightly.

You’ll have to trust me when I say I have already solved this three times over the years.  The first time took a week.  The last time took less than an hour.  They were done far enough apart so that I forgot most of the details of the solution, but having a vague memory of it certainly helped on the second and third efforts.

Maybe you have a better way.  Just remember, do not use a computer!  This must be solved by hand.

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