So, I get this email from Benj today. As if I didn't have enough things to help me procrastinate from my real objective tonight.

Basically, it's an optical illusion/puzzle where the image changes from 12 little men into 13 men and it's hard to figure it out.

http://www.drizzle.com/~mateo/1213.gif

Just in case the link gets deleted, here's the image that the link goes to:



I tried to figure it out and I couldn't. I knew that we were cutting faces and feet and stuff in half, but couldn't figure out where the 13th man came from, so I followed Benj's link to where a solution was:

http://www.defectiveyeti.com/archives/001258.html

This guy Matthew Baldwin broke it down to the point where I could understand it. It's lucky because I was going to break it down in photoshop and trace body parts anyway. This guy already did it for me.

For the sake of completeness, I've copied his image here in case he deletes it in the future. If he gets upset at me and asks me to take it down... i will. I'm going to post my update to his site in a minute.



So, to better understand his drawing, I created an extension drawing off of his that should clarify the whole puzzle quite simply...



Basically, the puzzle works by cutting each person in two, taking a small slice of them (1/12 of their height) and passes it over to the right until after 12 people you end up with a whole extra person. Then the creator mixed up the order of the people so that you couldn't see what he did and tada, you've got a puzzle.

Enjoy..
Jon

I don't get it - by Paul on April 20, 2005

I don't understand why this is so complicated. Am I missing something? One guy loses the top of his head and doesn't get it back. Another guy loses the bottom of his feet, and doesn't get them back. That's where the extra person comes in.

The point is, before the switch there are 12 full guys. After the switch there are 11 full guys and 2 guys who are only 11/12 complete. The 1/12 missing isn't obvious, which is why it works.

One more time with Math - by Jon Parish on April 21, 2005

Hey Paul,

This should help:



It's not 11 full guys plus two that are 11/12 complete. It's actually 12 guys that are 11/12 complete plus one guy who is 12/12 complete. Each man is missing a slice except 1. The guys without the hair and the guy without the bottom of the shoes are just missing the slice on the end, making them more noticable.
For instance:
guy 1 is missing his scalp,
guy 8 is missing his forehead,
guy 4 is missing his eyes,
etc.

If you add up all the pixels you took out of the other guys, you end up with the pixels that create the extra man. Personally, I feel sorry for guy no. 5 who looses his wee wee.

Super Search Engines - by Jon Parish on April 25, 2005

For the longest time, I didn't think Google liked me. I haven't really added any new pages in ages, and I think they modified their scoring algorythm to discount sites like mine that have lots of links in it to it's own pages.

Anyway, I just got on Google uber quickly. Here's the timeline:

April 19th, 2005 9:00 pm EST - I post the story
April 20th, 2005 5:00 pm EST - No. 1 on Google for "12 13 man puzzle" searches
April 23rd, 2005 4:20 pm EST - No. 1 on Yahoo for "12 13 man illusion" I haven't kept up with the interworkings of Yahoo and Google's search results.

Others have filtered in too including Dogpile (combines results from multiple search engines), AOLsearch (which I think is just Google branded under aol), searchalot (similar to dogpile?), etc.

Still no word from msn, or the other big name crawlers.

Actually it is 12/13 - by Ueli Wahli on April 26, 2005

You say: It's actually 12 guys that are 11/12 complete plus one guy who is 12/12 complete.

Looking at the drawing, the new guy is not complete, missing part of the feet. So I would say, each guy looses 1/13. So the 12 original guys are now 12/13 as big, and the new guy is 12/13 as well. So we have 13 guys of 12/13 size, which equals the original 12.

Actually, it's not - by Jon Parish on April 27, 2005

Hi Ueli,

I don't want to split hairs here. Especially if the difference is on the order of half a percentage point difference between our generalizations (1/12-1/13=.6%).

Since you're into the math, let's take it the next step... Algebra.

Problem:
Where did the extra man come from?

Given:
No matter how many pieces we cut them into, the sum of their heights is always constant.


New guy's height is always the old guys height minus the difference between their heights.


Solution:







Q.E.D.


For those of you who don't do algebra, I just proved that the height of the 13th man is equal to the sum of the changes in height of the original 12. We don't care how much each man shrunk, just that the total shrinkage of the original 12 men = the total growth of the 13th man.

LIKUWI: The Extra Man Puzzle - by Belford Boles on May 25, 2005

In searching for information of people working together to solve and/or discuss the Extra Man Puzzle, the Corporate Super Hero web page was found. The Corporate Super Hero web page provides observable and mathematical explanations of the Extra Man Puzzle. I have put this information in web log http://bloghoopla.com/?u=folderb.

where did the man go puzzle - by John Gualtieri on April 12, 2006

You won't be able to figure it out until you have the puzzle in front of you in your hands and can move the pieces yourself. Then all you need do is add up the men plus the fractional men for both positions. Then you will see that the number doesn't change at all. It's just a clever cover-up to make it seem that there is a loss of a man.This is an old puzzle, that I once had both pieces to, but, I lost one piece, so I can't prove it to you.

wow!! - by alizeh on November 10, 2006

what a cool puzzle i didnt read the whole explainations n stuff...but i kinda got a li'l sumfin....neway its soo cool 2 c sooo many ppl making such a big deal outa dis thin..peace out y'all!!!

this is it basically explained for normal people - by luke13 on November 16, 2006

This is what happens.
1st guy passes on a bit of his head
next guy passes on more of his head than the first guy passed on
3rd guy passes on more of his head than the second guy passed on
4th guy passes on his whole head
5th guy head and shoulders.....so on
....
11th guy passes on all but his feet
12th guy passes on all but the soles of hes feet and what he passes on we see as an extra person.
The only reson we dont notice this illusion is because its such a small different with each pass to the next person.
There no fractions involved!

this is it basically explained for normal people - by luke13 on November 16, 2006

This is what happens.
1st guy passes on a bit of his head
next guy passes on more of his head than the first guy passed on
3rd guy passes on more of his head than the second guy passed on
4th guy passes on his whole head
5th guy head and shoulders.....so on
....
11th guy passes on all but his feet
12th guy passes on all but the soles of hes feet and what he passes on we see as an extra person.
The only reson we dont notice this illusion is because its such a small different with each pass to the next person.
There no fractions involved!

cool - by wreckz on November 21, 2006

this is very cool stuff..

LIKUWI: The Extra Man Puzzle Update 001 - by Belford Boles on March 8, 2007

Previous by Belford Boles on May 25, 2005 was
"In searching for information of people working together to solve and/or
discuss the Extra Man Puzzle, the Corporate Super Hero web page was found. The
Corporate Super Hero web page provides observable and mathematical explanations
of the Extra Man Puzzle. I have put this information in web log
http://bloghoopla.com/?u=folderb".

At time 2007/0308, the web log information is missing.
At time 2007/0308, information about the Extra Man Puzzle is at
http://www.folder-b.org/pg_004_TEMP_01.html and also
http://www.folder-b.net/pg_092_MB_01_FBSWP_OI_02.html.