Puzzle 10

[Radio]

Found this on FB and thought it was cute. FB comment says it's a trick because the matches do not touch. I don't like that answer.

I like these kind of puzzles. 24 hour rule.

[NN5I]

I'm fairly confident of my answer. Aaargh -- 24 hour rule! There is an easy systematic way to solve it.

But whoever originated the puzzle fails the grammar test. 90% fail, not 90% fails.

[wa8yxm]

I always wonder about those. the problem is there are two ways of answering.. The obvious answer and a hidden answer, I think I have both but alas. No posting will happen here.

[NN5I]

Originally Posted by Radio

FB comment says it's a trick because the matches do not touch.

The FB comment is off base. The puzzle doesn't ask How many squares are perfectly represented, it asks How many squares do you see.

There is a slightly trick answer if my count is correct -- but it's a linguistic trick and not a geometric trick. The question ought to have asked, How many squares are shown?

[Radio]

Well I haven't counted my squares just yet so I have no clue, but I did look at the clock and 24 hours are about up.

Some of the matches are "missing" and the empty spaces form rectangles. I did note a tendency on my part to count the rectangles as squares. Be careful. And I noted the missing matches were chosen quite carefully to create specific patterns. I wonder if that was done to exploit our tendency towards a certain kind of error.

First guess, anyone?

[NN5I]

I count 16. Since 16 is a square (the square of 4), maybe you could say there are 17.

Systematic attack: examine each node to see of how many squares that node is the upper left corner. Add the counts.

Then, as a check, do the same, counting for each node the number of squares for which it is the upper right corner. Add the counts, and the total should be the same.

Here's an annotated copy. Next to each node I have placed the number of squares of which that node is the upper left corner.

There are nine squares with sides of length 1.
There are five squares with sides of length 2.
There is one square with sides of length 3.
There is one square with sides of length 4.

Total, 16.

I also corrected the bad grammar.

[wa8yxm]

Thanks, that is what I got, Sixteen... I still do not like those types of puzzles.

[NN5I]

Originally Posted by wa8yxm

Thanks, that is what I got, Sixteen... I still do not like those types of puzzles.

I like'em.

[Radio]

Originally Posted by wa8yxm

Thanks, that is what I got, Sixteen... I still do not like those types of puzzles.

Oh you're going to LOVE the next one!!

[NN5I]

What's it gonna be, Wade, huh? Huh? What's it gonna be?