I'm not sure "illusion" is the right word. Because you don't see something does not make it an illusion.

It is a mind/ math puzzle for sure.

I guess I will give a clue........

1) The "KEY" pieces are the red and dark green ones.
2) You can solve the puzzle by seeing the answer or mathematically prooving something.

Gotta love work breaks :)

tarzan: guessing: floated a melon across the river

triangles: it's optical trickery. You can actually see it if you look very very closely.

There's probably a better (more elegant solution), but here's some trig:

Red subtriangle: cos(theta) = 8/ sqrt(9+64) = 20.6 degrees
green subtriangle: cos (phi) = 5/sqrt (4+25) = 21.8 degrees
entire triangle: cos (rho) = 13/(sqrt (25+169) = 21.03 degrees

The angle of the entire triangle is not equal to that of either of the fractional triangles.

Actually, you can do this via slopes. It's more elegant :)

I'm not sure "illusion" is the right word. Because you don't see something does not make it an illusion.

An illusion is an erroneous perception of reality. What I first perceived as reality when I looked at the two big triangles turned out to be false. :)

Good idea HeaTransfer but not quite the right one.

Regarding Tarzan- I was thinking juggling at first but that wouldn't work as the force required to make them airborne would exert an opposite force in the other direction; adding to Tarzan's gross weight.

Regarding Tarzan- I was thinking juggling at first but that wouldn't work as the force required to make them airborne would exert an opposite force in the other direction; adding to Tarzan's gross weight.

I first heard this problem in junior high when we had no idea about newton's 3 laws - so just call it ignorance but that is the correct answer ;)

Very good HeaTransfer.

Mathematically you can prove the slopes are different for each triangle therefore altering the shape.

The optical trick is that the pieces do NOT make a triangle. It only looks like a triangle. If you put a ruler to it........you can see it.

I didn't know how to make it hidden in blue so I made the text white......just highlight the same way.

To make it hidden in blue use spoiler tags:
[spoiler]This will be in blue[/spoilre]

(Just spell spoiler right both times, I wanted to show as an example.)

If you look at the squares where the "hypotenuse" is, you'll see that it doesn't go through the same intersection of squares. As stated before, the line is not straight. It's deception.

Sorry I shoulda been clearer myself...

1) He's gotta get there ASAP or Jane will get mad - no time to go back and forth

2) No trees near the river - thus no vines

3) He can't throw em or they'll break

4) He can't roll them or they might break or fall off the bridge

5) Jane can't leave to help because the company has already arrived

6) And she can't send her company cause that would just be rude ;)
Simple, just juggle them keeping one in the air keeps the wieght down.

Simple, just juggle them keeping one in the air keeps the wieght down.
I'd be impressed if ken0042 didn't already post the answer ;)

I'd be impressed if ken0042 didn't already post the answer ;)
well i have no way to prove it, but I did not look ahead in the threads :)
It was a memory thing, heard it a while ago.

well i have no way to prove it, but I did not look ahead in the threads :)
It was a memory thing, heard it a while ago.

Alright, we'll go on the honor system :)

This is an extremely hard one. I have found the answer however the explanation is beyond my mathematical knowledge.

A person walks into a 7-11 store and buys 4 items. He gives them to the clerk and he multiplies them and says $7.11 please. The guys says you can't do that. You have to add them up. The clerk apologies and adds them up. $7.11 please.

What is the price of the 4 items.


GOODLUCK!

Hmmm I think this is like sticking a square peg into a round hole:-)

This is an extremely hard one. I have found the answer however the explanation is beyond my mathematical knowledge.

A person walks into a 7-11 store and buys 4 items. He gives them to the clerk and he multiplies them and says $7.11 please. The guys says you can't do that. You have to add them up. The clerk apologies and adds them up. $7.11 please.

What is the price of the 4 items.

GOODLUCK!

wow thats a toughy, do i rack my brain with the math or is there a simple answer
Is tax applied?
If the cost was with out tax each item would be 1.7775
of course 4x1.77 is only 7.08 so that would be 3 cents of tax or 0.75 cents of tax per item
thats some low tax :D

There is no tax added.

I tried to figure out an easy answer. I still believe there is one however people a lot smarter than me did not have a simple answer.

Joe

Hmmm I think this is like sticking a square peg into a round hole:-)

worse!!

Here is just the answer

1.20, 1.25, 1.50 , 3.16

short description (http://www.casact.org/pubs/actrev/feb99/puzzle.htm)

there is a much longer description but I can't find it anymore.

Joe

wow thats a toughy, do i rack my brain with the math or is there a simple answer
Is tax applied?
If the cost was with out tax each item would be 1.7775
of course 4x1.77 is only 7.08 so that would be 3 cents of tax or 0.75 cents of tax per item
thats some low tax :D

Our mistake to start with is to assume that the items have the same price... that is the big part of the puzzle... Now I read the solution and It's too confusing for sure... :)