stolf’s blog 593: rectangles ?!?!?


You did the SQUARES…now how many RECTANGLES?

…bearing in mind that a square counts as a rectangle. At first this seemed like a daunting task, but once I got around to organizing a plan of attack, it wasn’t hard at all. Took me under 5 minutes. Really? Sure…let’s take it step by step…

And that plan of attack was to classify rectangles by their size, based on the unit square, seen below in red. Rectangles would be AxB…that is, A is the length down and B is the length across. Below for example we have 1×2 in purple and 3×4 in green…


Next, we list all the possibilities, remembering that we’ve already done AxA…those were the squares…

plan of attack

That’s 12 types of rectangles in all…but there’s a short-cut…we only have to count 6 types, then double that total. You can see why demonstrated below with 1×4…flip the puzzle on its side by rotating it 90 degrees, and you have the same number for 4×1 as you had for 1×4.


That’s pretty much all there is to it…take the rectangles type by type…count carefully and keep a running total.

1x2 1x3 1x4 2x3 2x4 3x4

Now add in the mini-rectangles…plus the 40 squares from the last puzzle…and we’re done…grand total = 118.



Copyright © 2012 Mark John, All Rights Reserved

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