ARRRGGH!!! Need help with a puzzle!

[Lauren Hynde]

I'll take your word on it. I bow and grovel before your geometric greatness. (Don't tell Vella . . . she might get mad that I groveled to someone else).
Again, I wonder if this illusion would've worked if we had a physical manifestation of the pieces rather than a drawing.

We may never know . . .

(Twilight Zone musics cued in the background)
(Fade to black)

Of course you would have worked it. You would have overlapped the two triangles, ran your fingers across the "hypotenuses", and felt the discrepancy.

 

[Lauren Hynde]

I've seen this one before, and had thwe solution explained to me, so I didn't want to spoil the fun by butting in too soon.

Lauren is right . One of those two (the one with the extra square, I guess) is in fact not a triangle. It only looks that way because it's almost one, and since we're told that it is one, we believe it. And if our eye-sight raises objections, our brain usually just tells it to STFU.

#L

Nikki is right-er than me. Neither of them is a triangle. One is concave, the other is convex. The deviation that I didn't bother to calculate only needs to equal the area of half a square.

 

[dr_mabeuse]

Geez, you guys are good. Thanks to all.

It's a nice site for optical illusions, huh? They work especially well on a CRT.

---Zoot

 

[Lauren Hynde]

And if our eye-sight raises objections, our brain usually just tells it to STFU.

#L

And come online somewhere. I have something for you.

 

[Guest]

The second "triangle" isn't a triangle. The hypotenuse isn't a straight line, it's slightly convex. It's very slight, but you can see it by the way the grid intercepts each of the triangles; that's where the extra area comes from.

(Took me about 2 seconds to figure it out. I guess studying architecture does pay off after all... )

Ok, I see what you are saying, but in this instance I don't see that it makes a difference. The base and the height are still the same and that is what was used in calculating the area. I see a convex hypotenuse on one and concave on the other, but the length and hieght are the same. So where does the empty square come from? If I could see one of the triangles having a half unit longer base and/or hieght it would make sense. But that's not what I am seeing.


Get some grid paper, mark the dimensions for each piece and cut them out. Put them together and see what happens.

 

[Evil Alpaca]

Of course you would have worked it. You would have overlapped the two triangles, ran your fingers across the "hypotenuses", and felt the discrepancy.

Hey! You're making math sexy! I didn't know that was possible!

 

[gauchecritic]

The puzzle I need help with is in the second row down, fourth from the left: the two triangles.
---dr.M.

Zoot, Zoot, Zoot, what are you like? and you an author!

If you look at the puzzle again and read what it says you will find that there is nothing wrong at all. It's simply not a geometry puzzle.

In actual fact it's a word puzzle along the lines of "Where would the survivors be buried?"

The representation is that they are two triangles and as you well know the lower figure is not a triangle, it's an irregular septagon.

 

[Guest]

Hey! You're making math sexy! I didn't know that was possible!

Doesn't she just, eh? Phwoar!!!

For Lauren:

 

[Lauren Hynde]

Geez, you guys are good. Thanks to all.

It's a nice site for optical illusions, huh? They work especially well on a CRT.

---Zoot

I got a couple in my email today, but not like this one. Here they are anyway.

Faces:

 

[Lauren Hynde]

horses

 

[Lauren Hynde]

horses

It's too big. Nevermind, it's stoopid anyway...

 

[Liar]

And come online somewhere. I have something for you.

In a jiffy.

 

[Evil Alpaca]

I got a couple in my email today, but not like this one. Here they are anyway.

Faces:

Dang it, I found 10 but I'm missing the eleventh!

 

[Guest]

Dang it, I found 10 but I'm missing the eleventh!

I only got 7, then my eyes went squiffy. But I am an eensy bit drunk.

 

[Liar]

I got a couple in my email today, but not like this one. Here they are anyway.

Faces:

Good one. I spotted ten. Does that make me cool?

 

[Lauren Hynde]

Ok, I see what you are saying, but in this instance I don't see that it makes a difference. The base and the height are still the same and that is what was used in calculating the area. I see a convex hypotenuse on one and concave on the other, but the length and hieght are the same. So where does the empty square come from? If I could see one of the triangles having a half unit longer base and/or hieght it would make sense. But that's not what I am seeing.


Get some grid paper, mark the dimensions for each piece and cut them out. Put them together and see what happens.

You're not understanding. The area of "triangle" 1 is smaller than the area of a real 13/5 rectangle triangle, because the "hypotenuse" is concave. The area of "triangle" 2 is larger than the area of a real 13/5 rectangle triangle, because the "hypotenuse" is convex. The added area of these two deviations amounts to 1 whole square, as is evident in "triangle" 2.

 

[Evil Alpaca]

Actually, I think I found all eleven now.

Yay for me!

 

[Guest]

You're not understanding. The area of "triangle" 1 is smaller than the area of a real 13/5 rectangle triangle, because the "hypotenuse" is concave. The area of "triangle" 2 is larger than the area of a real 13/5 rectangle triangle, because the "hypotenuse" is convex. The added area of these two deviations amounts to 1 whole square, as is evident in "triangle" 2.

I understand that the difference in total area is equal to one whole square. What I am trying to figure out is this:

If the base and height dimensions of the individual pieces are the same in both diagrams, and that's what I am seeing, how did the difference in area translate from a sliver off the top to a whole block in the bottom?

 

[Lauren Hynde]

I understand that the difference in total area is equal to one whole square. What I am trying to figure out is this:

If the base and height dimensions of the individual pieces are the same in both diagrams, and that's what I am seeing, how did the difference in area translate from a sliver off the top to a whole block in the bottom?

There is no difference in area... That's the point.

 

[NoJo]

Just looked through this thread. It's a very old puzzle, appeared in Martin Gardner's first book of mathematical puzzles and diversions in the late 1950's. I made one of these out of cardboard. Fans of the Golden Ratio will notice the Fibonnaci numbers in the sides of the triangle -- and will see how you can make an infinite number of variations of this puzzle.

The last puzzle to really stump me was a probability/games theory puzzle based on a real game show in the U.S. It's also pretty well known. If you already know it, don't give away the answer:

At the end of a game show, the contestant is shown three doors. Behind only one of the three doors is a prize.

The game show host asks the contestant to pick one of the doors.

Then, no matter which door the contestant chooses, the host opens one of the two doors remaining, to reveal that there's nothing behind that door.

The host then asks the contestant whether she wants to

1. Stick with her original guess, or
2. Switch her guess to the other closed door.

The puzzle is: Can the contestant increase her chance of guessing the door with the prize? And if so, what should she do?

 

[cantdog]

Your "half base times the height tipped me off. The two colored triangles HAVE to have a different slope from each other.

If you've pitched a roof, you'd have seen it. 3 rise in a length of 8 is not the same ratio as 2 rise in a length of 5.

So neither figure is actually a triangle, taken as a whole.

 

[NoJo]

Yes, but about those three doors...