The answer is: 40 squares…and seeing is believing!
Chart A…Where to begin? Well, apart from the mini-squares in the center, the smallest building block in the puzzle is what we might call a “unit square.” One of them is outlined in Chart A.
Chart B…And since the entire puzzle is a block of 4 unit squares horizontally and 4 unit squares vertically, that’s a total of 4 x 4 = 16 unit squares. We can call these 1×1 squares…that is, 1 square on each side. I know, since there’s only one unit square in a 1×1 configuration, how can you refer to “sides” plural, as implied by the phrase “each side”? It’s because of the curious but very useful mathematical fact that 1 x 1 = 1, that’s why.
Chart C…We then count the 2 unit squares in the center…
Chart D…And each of those is divided into 4 mini-squares…running total is now 26.
Chart E…We next move on to the 2×2 squares, made up of 2 unit squares to a side. Chart E shows there are 9 of them. What a lot of people do is consider just the corner 2×2′s…the ones labeled 27, 29, 33, and 35. But as you can see, there are 2 more “centered” horizontally, 28 and 34…2 more “centered” vertically, 30 and 32…and a final 2×2 completely centered, 31. Running total is now 35.
Chart F…With the 3×3 squares, there really are only “corner” ones, the 4 shown in Chart F. That’s because the total puzzle is made up of 4×4 unit squares, and 4 is an even number…and with the 3×3 squares, 3 is an odd number. If the total puzzle had been 5×5, then there would be room for additional “centered” 3×3′s, you see? But here there is not. Move the corner square 36 over one unit square to “center” it, and you now have another corner, 37. So the running total is up to 39.
Chart G… And finally, don’t forget the total puzzle itself, a 4×4 square…grand total = 40. Done and done!
PS: With 40 the definitive answer, some of you may be disappointed that there’s nothing left to argue about…but have I got good news for you! I read one comment that said the answer depended on the “rules”…and I thought: What rules? A square’s a square…4 equal straight sides, 4 interior right angles…pretty straightforward to me. Well, and you have to follow the lines given in the puzzle…nothing like this, for example:
But you know what? You should never underestimate the scope of people’s imaginations, however misguided. An earnest noodnik… whose website I will not dignify with a link, sorry…suggests there are 7 more “squares,” as follows…
The arguments pro and con are obvious, so I won’t go into them…except to say I’m sticking with 40. OK, I will say this: It reminds me of when I worked at a radio station and we broadcast a scavenger hunt…one of the items was a unicycle. A lady brought in a Christmas tree ornament of Santa riding a unicycle…she didn’t get credit. This was maybe 25 years ago and I’ll bet she’s still sore.
Copyright © 2012 Mark John, All Rights Reserved
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