[Dallas59]

HA HA HA! All your holes belong to us!

[Darkwolf]

I don't know good math talkin' but doesn't the red triangle's longer base make the "back" end of the triangle bigger in this arrangement, while not affecting the overall length? (Imagine a long car towing a small trailer--if you switch positions, the "long" part is in back now.)

[HairOfTheDog]

~scratches head~

[jdm]

In the top triangle, the green piece is below the yellow piece.

In the bottom triangle, the green piece is next to the yellow piece.

Such a change in placement would account for the extra square on the grid.

[MikefromOhio]

Count the squares the bottom of the red triangle takes versus the number of squares the bottom of the green triangle take up....

[YankeeinOkieville]

8:3 5:2

[Swordmaker]

A Two unit high by five unit long right triangle does not have the same angle at the top angle as a three unit high by eight unit long right angle. The first set up has a subtle but noticeable downward bend along the top side where the two triangles meet. When you reposition the pieces, the bend is reversed, bending upwards, adding area to the over all triangle. This differential is equal to one square unit.

[Graybeard58]

The shapes in the second figure are no longer interlocking. the interesting thing is that there is only one hole, because you can change the figures in any number of ways and create even more holes but the pieces would still be contiguous.

[dinasour]

The hypotenuse of the top triangle is not a straight line, but instead the red and green triangles make a small angle where they meet.

[Doctor Stochastic]

It's a Fibonacci number thing. The lines in the diagrams are not straight. The subtle differences in angle make up for 1 unit of area.

[jdm]

Anyone know the answer? This is driving me crazy!