Now how is THAT possible??

[Icetuete]

look at that

 

http://autsch.rtl.de/dumm_gelaufen/pixx/fehlendes_quadrat.jpg

 

now where did the missing square go??

[Icetuete]

dont mind the german sentences on the right. it justs says that these 4 pieces are put in two different orders. below it says "where did the missing square go?"

 

have fun

Edited June 24, 2003 by Icetuete

[ZR440]

It didn't go anywhere. The area is the same for both.

[Icetuete]

that is the point of this riddle. it IS the same area and at the same time it is not. or is it? who knows

[ZR440]

By rearranging the individual sections, it slightly changes the overall shape, but the combined area remains the same.

[capn_midnight]

the pieces still take the same area. The point is, the configuration is irrelevant.

 

This is similar to the Riddle of the Missing Dollar.

 

Three guests decide to stay the night at a lodge whose rate they are initially told is $30 per night. However, after the guests have each paid $10 and gone to their room, the proprietor discovers that the correct rate should actually be $25. As a result, he gives the bellboy the $5 that was overpaid, together with instructions to return it to the guests. Upon consideration of the fact that $5 will be problematic to split three ways, the bellboy decides to pocket $2 and return $1 each, or a total of $3, to the guests. Upon doing so, the guests have now each paid a total of $9 for the room, for a total of $27, and the bellboy has retained $2. So where has the remaining $1 from the initial $30 paid by the guests gone?!

[Icetuete]

y rearranging the individual sections, it slightly changes the overall shape, but the combined area remains the same.

 

i am not sure whether i did get u right... the rearranging does NOT change the shape. it cant because for the same reason that makes the combined area stay the same: the sum of the squares dont change in these 2 arrangements.

[Icetuete]

the pieces still take the same area. The point is, the configuration is irrelevant.

 

yes indeed - so how can it be possible that suddenly one square is missing?

[Icetuete]

and btw: i like ur missing dollar riddle. its rather old, but a real good one!

[ZR440]

What I meant to say is that the only possible explanation for losing or gaining area in this example would be for one or both of the hypotenuse being concave or convex, because if you match a grid square against another corresponding grid square, they look different. It's some kind of illusion.