Conundrum #Digamma

[nickcosmosonde]

Here's an interesting headscratcher. Draw an 8x8 square on graph paper and divide up as in the first image. Cut out the four shapes and rearrange as in the second, making a 5x13 rectangle.

Where did the extra square come from?









Sorry, I can't figure out how to size these pics properly - maybe Bets or her Ladyship knows how and would be so kind.

I shrunk the very large thing. I can hardly see the very small thing. But good attempt. C+ - LMH

[rjpageuk]

The second pic is so small it is hard to see.

It cant be resized as the original is of poor resolution to start with.

[nickcosmosonde]

That's odd, it's shrunk since I posted it. It doesn't matter - you can see it, can't you? Turn A and B over, put A next to C and B next to D in a 5x13 rectangle, and voila.

[rjpageuk]

I was hoping this thread would generate some discussion as this is a very cunning problem.

I believe the answer is that the triangles A and B in diagram two are NOT congruent to the triangles in diagram one, in fact they are not triangles at all.

The diagonal line between shapes C and D is not at the same angle as the diagonal line between A and B, and therefore the triangles in diagram two are actually quadrilaterals.

The extra square comes from the space gained through this.

[nickcosmosonde]

I was hoping this thread would generate some discussion as this is a very cunning problem.

It's a fun one anyway - I have had much amusement over the years infuriating people with it. Teenage boys like my nephew are especially good fun - he was in a tantrum for hours about it last week. You've just got an A* in maths, you work it out, dummy, I said. It's something to do with Fibonacci isn't it? he begged. Fibonacci my arse, I thought you were supposed to be bright?

I believe the answer is that the triangles A and B in diagram two are NOT congruent to the triangles in diagram one, in fact they are not triangles at all.

Huh? RJ, the idea is to draw diagram one and cut out the shapes, see? They're congruent because they're identical. And they are triangles - if they're not, draw them properly this time.

The diagonal line between shapes C and D is not at the same angle as the diagonal line between A and B, and therefore the triangles in diagram two are actually quadrilaterals.

Fibonacci was a better answer, old chap, but good go.