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Birthdays

A friend sent me this animated GIF.

1) Count the number of characters before the motion begins.

2) Watch the animation.

3) Count the number of characters after the animation ends.

4) Explain it to me... please!

Views: 259

Replies to This Discussion

It hurts.

It fucking does!!!
Where does the 13th fellow come from ?!?!?

The 5 on the right is always the same, the only row that changes is the second.

Sure.

At A) you have five on the right, two in the middle, and five on the left.

but at B) you still have five on the right, still two in the middle, but six on the left!

WTF?

 

13 before and 12 after! Someone is lost here! Where is he? :D

Haha! I don't know! It's an illusion O_o

OK - I know - well not quite but I think I've figured something =)

And it's incredibly clever. I have no idea how they came up with this... and I had to use brute force to figure what they do, not intelligent deduction. I tracked just the heads and feet.

It's all in the way they position each figure along the horizontal split line. in A The line cuts twelve different body parts on each figure. When they reconstitute the image in B, each has shrunk by a twelfth of its height and  - thanks to the even cleverer vertical positioning of the figures - a thirteenth fellow pops out of nowhere.

Click to enlarge

I clearly don't understand how they achieved that in the first place but I still think it's just plain awesome. 

Well first, you are a master at graphics and two it is really awesome. I couldn't get that far. I thought it has to do with the legs and heads but I couldn't explain beyond that.

Like I said, I can barely explain it myself. I have no idea how the thirteenth guy visually gets his twelve body parts, as they don't move independently.

That's pretty much the limit of my non-math method =/

And I'm almost certain that if someone was to explain to me how it's done, I wouldn't get it.

I missed this yesterday :-( Too busy. I commend you on your approach, Michel, I was going to do the empirical thing to do which is label the heads and the feet. What is happening is that you are moving a row of 3 into a row of two, but the original row of 3 from which the "13th" guy moves, does not change from 3 to 2 because the front guy never moves. 

One of the characters are being "split in two" in the animation, which is how you go from 12 to 13 characters.

The animation breaks the original image into 3 parts, then re-assembles them. When the image splits, each person is either split into 2 parts, or left intact.

If they're left intact, then they can't change the number of people in the image no matter where you move them. So we can ignore them.

So, in the animation, some people are split in two.

In order to preserve the number of people before and after the animation, the pieces must be assembled such that each "half" of a person must be connected to exactly one other "half" of a person.

But this isn't the case.

Look at the image when there are 12 people in it - specifically, at the smiling man in the black tanktop toward the top right.

When the image splits, the bottom of his feet is split off.

When the image re-assembles, he isn't attached to any other part of a person - his feet are just missing a piece. But because that piece is small (and the drawing quality is already dodgy), it's easy to overlook. So while someone else is being attached to his feet, he's being set apart on his own - and so we have an extra character.

This is easy to demonstrate, if you're so inclined:

If you have an image editor, make every person a different color. At the end of the animation, everyone who was split in "half" and re-assembled should be two colors - but this guy will only be one.

Or, print out the image when there are 12 people in it - and cut it into 3 pieces, like with the animation, but make the horizontal cut somewhere other than where it happens in the animation. It becomes clearer that he's missing "half" of him.

Can I brag, please? Half of this commenter's DNA is MINE. He came up with this answer in 10-15 minutes. Clearest explanation ever. *end of my shameless bragging*

Must of been Nail's half that solved the problem. =)

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