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Put it in the B configuration. There are 12 boys, which can be thought of as 24 halves bundled in pairs: a half on the outside of the circle, and a half on the inside of the circle. (Conveniently, also, each bundled pair of halves includes one half with a flag and one half without a flag). Some of these halves are more substantial looking than others, mind you. Rotate it to the A configuration: There are still 24 hal…
Which boy is gone? :)
Earlier quoted context omitted.
The flags don't really "do" anything. In the one configuration, every flag is held by a boy. In the other configuration one boy has no flag, and there is a severed hand holding a flag.
That's actually wrong for the other configuration. In one, every boy has a flag. In the other, there's one boy with no flag, and 12 boys with flags. The appearance of a boy with no flags is an insight.
The diagram's inner disc contains one complete torso with arms and hands, which holds two flags in either configuration, so "every boy has a flag" is only true if you actually mean "has at least one flag", not if you mean "has one flag".
Since the number of flags is not affected by configuration, one boy not having a flag is unsurprising. There are always 13 flags, so if there are apparently 13 boys, and one is still holding two flags, then someone must necessarily not have a flag.
(In the A configuration, there are actually two boys with no flags. One clutches his head with both hands, holding no flag, and the other, next to the A, is flanked by a floating, detached hand which holds a flag. Therefore, that boy has no hand, and no flag. This severed does not seem essential, either; I believe the picture could be somehow repaired so that the detached hand is reattached. Then in the A configuration would be exactly one boy with no flag, as you say.)
Earlier quoted context omitted.
My guess: The problem is one of discrete values. You are asking about "a boy", but there are no "a boy"s. There are only fractions of boys. The total sum of "boy fractions" is the same, but the number of pairs of "boy fractions" that meet the distinction of "a boy" changes. "A boy" does not vanish because there were never "a boy"s in the first place. One might have better luck with "boy heads", and you can see that a…
I also couldn't help but notice this after reading your comment, but in the image it seems pretty clearly that the A configuration is pretty incoherent. The 5 o'clock boy you mentioned, for example, clearly has a sleeve for the right side of his face, the boy at 2 o'clock is also missing a large chunk of his head, and of course the two boys at 8 o'clock overlap, but, now that I look again, in an incoherent way. To me…
If done right, the idea is that in the one configuration you have thirteen 24/25ths of a boy, so thirteen 96%-boys. You hide this as each one being slightly skinny.
In the other configuration you have twelve 26/25ths of a boy, so twelve 104%-boys. You hide this as each one being slightly fat.
The danger is that if you make the drawing too detailed and gorgeous, someone will be able to look at a little detail like eyes or so, if one of these 4% slices contains an eye then you may end up with boys with 1 or 3 eyes, something that any looker would say spoils the illusion.
You have a couple options there.
- People will accept a "dead zone" where the two moving parts interact, you can try to locate an eye inside the "dead zone" so that you don't trigger this W-T-F moment.
- Use cartoonishness/ambiguity. So maybe this dot means "eye" on this cartoon but "freckle" on that cartoon, similarly by locating the exact eye on the border between the two, maybe half a line goes from being "long eyelashes" to being "the middle of a winking eye" or so.
Unfortunately this doesn't work with banknotes ... unless you can find lots of people who are willing to accept a banknote that appears to have been torn into two pieces and then stuck together again with sticky tape, with the line of the tear being a weird curve that just happens to cross both serial numbers in roughly the same place.
That sounds like something from Martin Gardener, I definitely heard of this trick!
Unfortunately this doesn't work with banknotes ... unless you can find lots of people who are willing to accept a banknote that appears to have been torn into two pieces and then stuck together again with sticky tape, with the line of the tear being a weird curve that just happens to cross both serial numbers in roughly the same place.
‘Nobody’ looks at banknotes. Also, historically, banknotes were torn and repaired more often. Because of that, you can just cut a 1/10th width strip out of 9 banknotes and glue them together to make a 9/10 width tenth banknote. Examples: https://books.google.com/books?id=e7QzAQAAMAAJ&pg=PA318&lpg=... (1804) https://books.google.com/books?id=osjhDwAAQBAJ&pg=PA114&lpg=... (1850s) A more tricky recent variant replaces t…
I was pretty confused until I noticed the bottom right head turning into an arm.
Part of the trick is that the boys are split into two parts and progress from more inside to more outside along the wheel. Since the unit "a boy" is based on real world experience where boys can be different sizes and especially since how much space a boy takes up in an image can vary depending on angle, we mentally accept that this mashup of different amounts of body parts adds up to "one boy" rather than thinking "…
1+12, 2+11, 3+10, ..., 10+3, 11+2, 12+1
(12 pairs, each adding up to 13)
0+12, 1+11, 2+10, ..., 10+2, 11+1, 12+0
(13 pairs, each adding up to 12)