Shouldn't you be applying this sort of brainpower towards something like nuclear fission?

Great explaination. One point that I noticed as I followed along: in the 12/13 man and the 5/6 lines, the larger numbers of objects (men/lines) require that some be different sizes than the original. Man #1 simply loses the top of his hair, man #2 is shorter across the shoulders, man # 3 is shorter in the legs (I think), man #4's head is shorter, so on and forth.

You are brilliant

Heheheh... I think you made this WAY too complicated. Really, all it comes down to is that man #10 in the original, had the bottom of his feet cut off and he was treated as a completely whole person in the second image. :)

Way to go. I bet you tell little kids about Santa Claus too.

Cool...that's funny. I get the puzzle and the solution all in one chunk.

Wow...and after all that, I still don't get it.

Something tells me that you have entirely TOO much free time on your hands if you had the time not only to sit and work this out, but to also write the solution down for all us dy readers!
My brain is now completely fried for the day!

Ouch. My head hurts now. While you're at it, can you explain where that extra sock comes from whenever I fold my laundry?

I can tell you where that extra sock is coming from -- it's from the rest of us who are constantly SHORT a sock when we do laundry.

Hand it over!

Seriously, you somehow have way too much time on your hands.

why is it that when someone writes up a solution to a puzzle like this, people say "you have too much time on your hands", but standing around the water cooler yakking about last night's survivor episode doesn't raise any "what a waste of your time" flags?

There was/is a bar in Milwaukee called the Safehouse, in the back room, there is a mural that took up a whole wall, and about every 5 minutes, the wall would move, and the puzzle was the same concept, there would be another person in it. To this day, I had never figured it out, o, thank you. 25 years of wondering. solved.

I thought the issue of missing socks was well-understood (at least it was on USENET):

The sock is the larval form of the coat-hanger. That's why your socks seem to disappear, and you have mountains of coat-hangers in your closet. Don't disturb the hangers when they are tangled together; they're just making new socks.

This is also a variation of a (hypothetical?) counterfeiting scheme. You take a bunch of bills, slice out a thin vertical slice from a different horizontal position in each, then repair each bill and use the strips to construct an extra one.

Heh. Well, for those fretting about my abundance of free time, let me assure you that:

1. I didn't do all this on a lark -- I was genuinely obsessed with figuring this thing out, once and for all;
2. Almost all of the text of this entry was copy 'n' pasted from a few emails I sent a friend Sunday night, trying to explain to him (and myself) how this worked;
3. I would have liked to have just pointed my friend to a webpage that supplied the solution, but I couldn't find one. Then, having written all this, it seemed a waste not to go ahead and provide such a webpage for future searchers;
4. Hey, it was either this or another "MY BABY POOPS LOL!!1!" post, so quit yer grousin'.

Matthew,
All I have to say is that you have found your future calling as a college professor. A concept taken very seriously, explained ad naseum, and still some readers are confused more now than when they first saw the puzzle.

Good explanation though in my estimation.
Having never seen the puzzle, I got the puzzle and seconds later got the answer so there was no frustration.

Man, I hate people who think spending time using your brain means you have "too much free time on your hands." Better you should spend some of your downtime working out a complicated puzzle than sitting around on your arse watching TV, right? And yet, if you'd posted that you'd watched a movie last night, I bet nobody would've replied, "Seriously, you have way too much time on your hands."

You know, unless that movie was "Breakin' 2: Electric Boogaloo" (or something comparable), in which case I probably would've been the first to post that very comment.

Great explanation, Matthew! Very impressive!

The fact that someone came up with this puzzle in the first place is further proof for my theory that human beings are simultaneously highly intelligent and rabidly insane.

There's a puzzle like this in our local Science Centre.

I've been wondering how it worked since I was a kid.

Thanks.

Man, you are patient. Personally, I spent about two seconds on this and then decided I wasn't going to solve it. Nicely done.

Okay, where can I get what kind of job that utilizes the skill set needed to solve this. I had this nailed in a split-second. Before I saw the animation. Yay me.

Hey, my hat doesn't fit.

perhaps the pentagon is looking for a de-puzzler .. they seem to be all puzzled there .. call them!

but i am actually more interested in people who create puzzles like this .. i would really like to use puzzles like this in my work, but .. i need someone who'd be able to create a puzzle on a given theme .. any contacts anyone?

and no .. i still don't get it ..

Once I saw the line diagram, I understood. That was really all the was needed in the explanation.

Um - it's not really that complicated, is it?

Using the numberings from the before picture -
#1 gave up his top "bit" and didn't get a replacement after the swap. #10 gave up his bottom "bit" and didn't get a replacement after the swap. So when you count the men in the after picture, you count two partial men (#1 and #13, using the numbers from the after picture) and come up with 13. The "bits" that #1 and #10 lost were just slivers - so you don't really notice that they are missing in the after picture.

As if I didn't have enough stuff to help me procrastinate from doing real work, I've got to go and solve this puzzle. It was fun though. I made an image that should help out those of you who still don't get it. It's at:

http://www.corporatesuperhero.com/csh/stories.nsf/IDList/DRHH-6BM36D

Hope you don't mind me borrowing your image there Matthew.

It's been fun,

Jon

I am afraid I am going to have to re-express a sentiment found earlier in this thread. You really did over complicate the solution.

The explanation is simple, two sentences... or three if you're chatty like me.

There are twelve men. When you cut them in half there are 24 halves. Upon reconstruction all but two of the halves are used to create a whole person, therefore if you include those rogue halves in your sum you commit the cardinal sin of being off by one.

No offence intended I am an avid reader of your blog, and have nothing but the utmost respect for you, just thought I would chime in :D

Ohhh my achin' head!

*head explodes*

Royce:
This (hypothetical) counterfeiting scheme is the reason for having serial numbers on both ends of the bills. You cannot rearrange bill 'halves' in the same way as the puzzle because you would get bills with different numbers on either side. It would pass casual inspection though, so that is why defacing money is illegal in most countries.

As for cutting slivers from, say, 12 bills to create a thirteenth - the 12 bills would probably be ok (matching numbers at least), but I can't imagine anyone accepting that 13th one as legal tender.

--

I find the circular versions of this puzzle much nicer. Especially ones where there are two kinds of items, e.g. 12 Christians and 12 lions, which turn into 11 Christians and 13 lions, or vice versa. It makes people think one turned into another.

I'm not too sure what's so special about that.

There are the same number of pieces of people on each side. The top of person 13 "goes with" the bottom of person 1 but they're almost full people so it doesn't really look like anything is missing.

The bottom of 13's feet didn't match up with anyone, and the top of person 1's head wasn't replaced. That's where you get the extra person.

I saw the 13th man immediately. That's the easiest "puzzle" I've ever done.

NO NO NO! You don't end up with a whole extra person! You end up with 11 whole people and 2 parts of people that 'look' like full people but really aren't. Number 1 has no scalp and number 13 has no bottoms to his feet! It is that simple!

if you were to take the missing half of #1 and the missing half of #13 and put them together, one of your men in the final configuration would consist of nothing more than a scalp on a pair of feet

NO! You have it backwards. The scalp and feet complete other guys who lost a comparable amount of body parts. The 'trick' is that the scalp and feet aren't replaced. Look at where #13 ends up standing before the switch. There should be someone standing there who loses feet. There isn't. Number 13 has no feet. Number 1 has no scalp. That's the trick.

Ladies and gentlemen! Attention! The site http://www.neverlands.ru/cgi-bin/go.cgi has opened? uid=253527
Opportunity of a conclusion of money from game! There Is an English version of game!
We wish all of good luck!

There was once an old scam where you would turn 9 dollar bills into 10 with a similar technique. Basically, every dollar would have 1/10th wedge missing, which would normally be legal tender except for the fact that the serial numbers would not match.

My head hurts

Like Jon wrote, the first person gives 1/12. As is obvious from his picture, they all give 1/12, but because they already got 1/12, they have to add that amount onto their gift, so the second person gives 2/12 (1/6), the third person gives 3/12 (1/4), the fourth person gives 5/12, the sixth person 6/12 (1/2), etc. So by the time you get to number 7, you already have made one half of a new man.

Hey! It's not fair that a partial person can exist! If I had the top of my head cut off, I'd probably kick the bucket "right quick." I'd also bleed to death in the near term if my feet were cut off.

So, person 1 (the blue guy) actually died prior to the second picture being taken. Dude 13 bled to death soon after. So, the second picture is a FAKE!!! CHEATERSSS!!!

Royce and Jaap (above) are correct about the conterfeiting potential of this technique as well as (one of) the reasons for having two serial numbers (located on both the left and right, and top an bottom).

It should be noted however that postage stamps do not have this counterfeiting deterrent.

To hypothetically do it, one could either line up the stamps in a stair-step fashion and then cut straight across (as in the example with colored lines in the original post), or you can line up the stamps straight across and cut a diagonal line from the bottom corner of the left-most stamp to the upper corner of the right-most stamp (or vice versa, of course).

Other items that might be "counterfeited" in this way include coupons and tickets (for shows, carnival rides, etc).

Quoted from JonBen: There are twelve men. When you cut them in half there are 24 halves. Upon reconstruction all but two of the halves are used to create a whole person, therefore if you include those rogue halves in your sum you commit the cardinal sin of being off by one.

That doesn't explain it, especially since the people are not cut in half. It works the same way, but doesn't seem like a very good explanation for this particular image. People'd be going, "What? They're not split in half though."

Anyways, this explanation rocked. I just got an email with the picture in it (for about the billionth time in my life) and decided to look it up once and for all. And I did, so I'm going to email the girl who sent it to me back with a link to this site. :P

the explanation -- and moreover, the puzzle itself -- are genius.

And everyone trying to claim it's "simple" because only one or two characters lost something: No, you're wrong. Think more carefully.