12 becomes 13

Mudbug

Administrator emeritus
Original poster
Jun 28, 2002
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North Central Colorado
I admit - I haven't spent hours and hours trying to figure this out, but it's starting to bug me now. Can anyone explain how it is that there are 12 people in this picture, then after they all move around, there's 13? I'm sure it's an illusion or something, or I should drink less... either way - I'd love to know how it's happening, and I'm too busy to dissect it.

P.s. - the image is supposed to be animated, but apparently the forum preview thingy doesn't do the animation - click it to see what's happening.
 

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SiliconAddict

macrumors 603
Jun 19, 2003
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Chicago, IL
I don't think its possible. Count heads. I think there is a frame or two in there in the GIF where someone is adding a person. Probably during the slide from right to left and left to right. Someone simply needs to break out the GIF into its simple frames. I'm pretty sure its a nice slight of hand trick.
 

sushi

Moderator emeritus
Jul 19, 2002
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Mudbug said:
I admit - I haven't spent hours and hours trying to figure this out, but it's starting to bug me now. Can anyone explain how it is that there are 12 people in this picture, then after they all move around, there's 13? I'm sure it's an illusion or something, or I should drink less... either way - I'd love to know how it's happening, and I'm too busy to dissect it.

P.s. - the image is supposed to be animated, but apparently the forum preview thingy doesn't do the animation - click it to see what's happening.
Check the ones where three becomes two and vice versa (column wise).

Nice optical illusion.

Sushi
 

sushi

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Jul 19, 2002
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sushi said:
Check the ones where three becomes two and vice versa (column wise).

Nice optical illusion.
I should add.

It's 3, 2, 2, 3 & 2 for a total of 12

Then it's 3, 3, 2, 3 & 2 for a total of 13

Check out the top of the head for the first one in the front when looking from left to right.

In the 12 mode he has a full head of hair. In the 13 mode he has a flat top. The missing head if you will -- which actually creates the additional head.

Sushi
 

atszyman

macrumors 68020
Sep 16, 2003
2,442
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The Dallas 'burbs
Unfortunately I cannot see an easy answer. You basically cut lots of people and now use half parts as whole parts to create another person.

Ok after spending way too much time on this it becomes a matter of where do you gain all of the extra body parts.

Face: the guy in the lower right corner loses his entire face in the move and gets it replaced with half of the face of the guy at the bottom in the first column of 2 in from the left. This is augmented by the guy in the lower left giving up the top of his head to cover the top of the guy in the column of 3 on the far left who loses the top of his head to cover the bottom half of the second guy listed in this convoluted description who loses only the top half of his face.

Legs: The guy on the far right cuts off at the knees and what's left become the legs for the guy in the top of the fist column of 2 in from the left.

Shoes : the top guy in the fist column cuts his shoes in half and they become the feet for the guy at the top of the middle column

Torso: The guy in the column of three furthest to the right cuts his torso in half and that becomes the torso for the head and shoulders of the guy in the middle of the column of 3 on the left.

Shorts: The guy that gets the legs cuts his shorts in half do be used with the top half of the first guy listed in torso.

When you start piecing all of these half cuts now used as full pieces you end up getting enough to build an extra person

Edit : you can only create the other person if your head has not exploded from trying to make sense out of my explanation.
 

SiliconAddict

macrumors 603
Jun 19, 2003
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Chicago, IL
Hmm

Note that the top of the guys head on the far left is the top of the guys head that has been altered.

Also second row from the left. Middle guy. His body isn't in the previous picture.
 

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latergator116

macrumors 68000
Sep 30, 2003
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Providence, RI
atszyman said:
Unfortunately I cannot see an easy answer. You basically cut lots of people and now use half parts as whole parts to create another person.

Ok after spending way too much time on this it becomes a matter of where do you gain all of the extra body parts.
I think that makes sense. Also, the guy in the lower right hand corner looks very strange without a mouth after the transformation.
 

russed

macrumors 68000
Jan 16, 2004
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wow that is confusing after a few wiskeys and half a bottle of wine
 

iMeowbot

macrumors G3
Aug 30, 2003
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Here they are as 3 layers in a photoshop file, so you can use the move tool to play with them. The animation isn't cheating, you can even print them out on paper, cut them out and play that way if you like.
 

Mudbug

Administrator emeritus
Original poster
Jun 28, 2002
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North Central Colorado
iMeowbot said:
Here they are as 3 layers in a photoshop file, so you can use the move tool to play with them. The animation isn't cheating, you can even print them out on paper, cut them out and play that way if you like.
I actually tried that before I saw your post (printing it out) - and it's just as baffling to me. I just can't wrap my head around it :D
 

iMeowbot

macrumors G3
Aug 30, 2003
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Here's atszyman's explanation in pictures.

(also, notice the feet of the two highest guys with black shirts. In the 13 view, the left blackshirt's feet are only the tops. the rightmost blackshirt's ankles are attached only to soles, no foot tops.)
 

Mudbug

Administrator emeritus
Original poster
Jun 28, 2002
3,809
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North Central Colorado
iMeowbot said:
Here's atszyman's explanation in pictures.

(also, notice the feet of the two highest guys with black shirts. In the 13 view, the left blackshirt's feet are only the tops. the rightmost blackshirt's ankles are attached only to soles, no foot tops.)
this is great - but I'm still getting lost where there's 12 faces in one version, and 13 faces in the other. I swear it's starting to make me feel a tad retarded that I can't follow it... :D
 

iMeowbot

macrumors G3
Aug 30, 2003
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It's just more of the same aplitting, honest =) In the 12-pic, second guy on the left, bottom row, his nose overlaps the margin so it can become a "whole" face when his head moves to the far right. Second guy from the right, bottom row, his eyes straddle the margin. That fills in the guy who used to have the overlapping nose, and the overlapping eyes still sitting on the bottom just need the hair from the poor scalped guy on the right to make him look sort of like a complete face (but he's missing a forehead).

That's really the whole trick right there, ambiguous cartoon features straddling the margin. Our brains want to see complete bodies so they sort of fill in features that aren't quite there.
 

Stelliform

macrumors 68000
Oct 21, 2002
1,721
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Mudbug said:
this is great - but I'm still getting lost where there's 12 faces in one version, and 13 faces in the other. I swear it's starting to make me feel a tad retarded that I can't follow it... :D
Also there are 12 pair of feet and legs in the first one, and 13 pair of feet and legs in the second one.
 

atszyman

macrumors 68020
Sep 16, 2003
2,442
1
The Dallas 'burbs
Let's break it down by numbers and see if my logic makes more sense

..1.....6..8..11
.2..4..7..9..12
3..5.....10

goes to

..a..d.....i..l
.b..e..g..j..m
c..f ..h..k

Person a = person 6 without shoes plus the bottom half of the shoes from person 1

Person b = head and shoulders of person 7 plus the torso/legs of person 2

Person c = person 3 minus the top of his head

Person d = person 8 minus the botoms of his shoes

Person e = top half of long torso on person 9 with the bottom half of long shorts/legs on person 4

Person f = bottom half of long head body from person 5 top of person 10's head

Person g = person 11 cut off at knees with shoes left from person 6

Person h = torso legs and shoes of person 7 with head from person 12

Person i = person 1 minus bottoms of shoes plus the bottoms of the shoes of person 8

Person j = bottom half of long torso from person 9 plus the head and shoulders of person 2

Person k =person 10 minus top of the head with top of head from person 1

Person l =head torso and top of shorts from person 4 with knees down legs from person 11

Person m = person 12 minus head plus top half of head from person 5

One set of shoes cut in half to make 13 sets of shoes.
Multiple head cuts with top half of person 5's head forming a full head with the chest of person 12, giving the 13th head.

Person 11's legs cut in half to get 13th set of legs.

Person 9's torso cut in half to yeild 13th torso. Person 4's shorts cut into two sets.

Someone may want to check all of my numbers but it should be pretty close.

Edit : added dots to preserve number spacing.
 

atszyman

macrumors 68020
Sep 16, 2003
2,442
1
The Dallas 'burbs
Mudbug said:
ok - I for one am thoroughly impressed. :)
how long did this take? (thanks :D)
Longer than any sane person should ever admit to having worked on this problem. ;)

Edit :
In addition to my insanity I am a very typical engineer and thus cannot leave a problem unsolved.
 

Doctor Q

Administrator
Staff member
Sep 19, 2002
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3,253
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Where it all began

Being a long-time puzzle fan, I remembered reading about an amazing puzzle that may have been the first of this type. It was called "Get Off The Earth" and was the greatest creation of Sam Loyd, a master puzzle maker from the late 19th century. He made not only mechanical puzzles but word puzzles, logic puzzles, mathematical puzzles, chess puzzles, and probably other types. There is even an annual Sam Loyd Award given to an entrepreneur for accomplishments in mechanical puzzles.

I managed to track down these details in the June 2000 issue of Game & Puzzle Collectors Quarterly.

The "Get Off The Earth" puzzle, from 1896, showed 13 Chinese warriors along the border of a rotating disc. When you turned the disc, one warrior disappeared. Millions of people were baffled and Sam Loyd sold over 10 million copies of the puzzle from 1896 through 1906.

The idea is the same as your 12/13 puzzle, and the headcount is even the same. I've attached a copy below. View it and watch it change from BEFORE to AFTER and back again.

If you want to print out a copy, see this page.
 

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zimv20

macrumors 601
Jul 18, 2002
4,388
7
toronto
solution for original puzzle

in scenario 1, there are 12 tops and 12 bottoms. they line up so we get 12 people.

in scenario 2, there are still 12 tops and 12 bottoms. BUT - the guy in position 1 (from the left) doesn't get a top, AND the guy in position 11 (from the left) doesn't line up w/ a bottom. since they're each 90% of a picture of a person, we count those two "halves" as two wholes, leaving an extra.

if we decide that each top must line up w/ a bottom, we declare scenario two broken, since only 11 of the 12 tops and bottoms line up.
 

Mechcozmo

macrumors 603
Jul 17, 2004
5,215
2
If you download a .gif and open it in Preview you can see each frame on its own.

FYI.