Anybody want to figure out the year?
The puzzle was originally conceived in 1906.
Love me some Sam Loyd, there is no greater chess puzzler in my mind.
Disappearing Bicyclist – Sam Loyd (1906)
21–30 of 66 posts
Re: Disappearing Bicyclist – Sam Loyd (1906)
#22Part 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 "No, that's just 85 percent of a boy and over there we have 105 percent of a boy!"
As someone else noted, we accept in one position that two partial boys each count as a whole boy and then in another position we accept that they each count as just part of a whole boy when paired differently.
(Edited in hopes of improving clarity.)
Re: Disappearing Bicyclist – Sam Loyd (1906)
#23Unfortunately 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…
If I had to guess they were using the five ask a test to a) see if it would pass a cursory inspection, which it appears it didn't, and b) refine the technique. People are generally more skeptical of larger denominations (especially 100 in the US which you can sometimes get a bit of grief over when trying to use), but if someone were to notice the 5 is counterfeit somehow it's not quite as suspicious just to pay with a different (legitimate) note.
Re: Disappearing Bicyclist – Sam Loyd (1906)
#24Put 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? :)
The inside boy at 8 o'clock. In position A he's there, in position B he's gone. Think of each position as a discrete state rather than thinking of it as "moving boys".
Re: Disappearing Bicyclist – Sam Loyd (1906)
#25Earlier quoted context omitted.
Which boy is gone? :)
The inside boy at 8 o'clock. In position A he's there, in position B he's gone. Think of each position as a discrete state rather than thinking of it as "moving boys".
Also the 2 o'clock boy has no flag in A then he has a flag in B.
Re: Disappearing Bicyclist – Sam Loyd (1906)
#26Unfortunately 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!
Re: Disappearing Bicyclist – Sam Loyd (1906)
#27You can isolate the discrepancy simply by considering just the bottom left quadrant.
When you flip configurations, an extra boy is shifted into the sector, forming the boy pair, so you can now count three boys in that sector instead of two. What is shifted out is just a fraction of a leg, so there is a net gain of one boy.
The remainder of the circle is constructed so that there appears is no net change in the number of boys there. The fraction of a leg which is shifted in replaces a fraction of a leg, and the boy which is shifted out is replaced by a boy.
But note that this is a paradox: you can't shift a leg into one end of a register, such that a person is shifted out of the other end, and yet have the person count in that register remain the same! That's like shifting a 0 into a bit register, such that 1 is shifted out the other end, yet the parity remains the same.
The subterfuge is that in configuration B, there is a Siamese twin body with two heads (A + 2 clockwise). The casual observer glosses over this, because the heads are fused together quite well, and counts them as one boy.
When the configuration is switched to A, this twin head is separated. There are no more Siamese heads sharing a body, and that separation is what keeps the apparent head count the same, even though a head is shifted out in compensation for a leg shifted in.
Another noteworthy feature is that when the boy pair is formed, it is also Siamese twins, sharing one leg. So in the A configuration we have Siamese twins sharing a leg, which gets counted as two people, but in the B configuration, we count Siamese sharing an entire body as one person, because the heads are so well fused as to almost look like one.
If you consistently count all instances of Siamese twins as either two people, or else as one person, then the count is consistently 13 or consistently 12.
The paradox here rests in a kind of "visual equivocation fallacy". The equivocation fallacy is that, during the course of counting boys around the circle in the two configurations, the observer's definition of whether a Siamese twin is one person or two changes, due to visual deception. Well-fused heads count as one person, but joining at the hip and sharing a leg counts as two people.
Re: Disappearing Bicyclist – Sam Loyd (1906)
#28A similar puzzle is Magic Microbes (ctrl-f it) from this page:
www.karlsims.com/puzzles.html
Re: Disappearing Bicyclist – Sam Loyd (1906)
#29See also the Missing Square puzzle: https://psychology.wikia.org/wiki/Missing_square_puzzle
Don't read the text if you want to figure it out yourself.
Re: Disappearing Bicyclist – Sam Loyd (1906)
#30Part 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 "…
To add to this, the boy at 3 o'clock, whose head is split in two equal pieces, is the key to the sleight of hand.
Does his head stay or does it move?
If it moves, the boy at 2 o'clock should count as 2 heads in position B. If it stays, then he should count as 2 heads in position B, since the head below him moves up.
But because it's ambiguous, we count it as both moving and not moving.