The Missing Dollar puzzle from Martin Gardner's Aha! Gotcha book series


#1

[Read the post]


#2

There are more pairs of records in the first pile of 30 records than there are triplets of records in the second pile of 30 records.

When you switch to sets of five records, you force there to be the same number of pairs and triplets.

To put it another way, when the clerk thought “5 for $2 is the same thing,” they were imagining a customer pulling two from one pile and three from the other, and paying $2. But if all the customers did that, you’d be left with ten of the more expensive records in the doubles-stack at the end of the day.


#3

I love the mark on the rod thing, although I think it would probably be simple to demonstrate that the precision of the measurement for even a very small corpus of text would require sub-quantum accuracy.


#4

Thanks; I couldn’t figure out how someone would get 5:2 for the average of 3:1 and 2:1.


#5

The '80s were so primitive. They needed huge metal rods to encode entire Encyclopedias! Now we encode them in the electron spins of pieces of exotic materials that are the size of a finger-tip.


#6

I like this missing dollar riddle better:

Three people are checking into a hotel and the clerk tells them it’s $30. Each person pays $10 and they head to the room. The clerk then realizes that the room is only $25, so he gives the bellhop 5 one dollar bills to return.

The bellhop doesn’t know how to split 5 bills among three people, so he pockets two of them and gives each person back $1.

So each person paid $9 for a total of $27 and the bellhop has $2 in his pocket. What happened to the other dollar?


#7

I did some rough calculations, and I believe you could encode an encyclopedia onto a gold rod about 1 meter long if you could measure the rod to an accuracy of 10 gold atoms (about 3 nanometers). Modern hard drives can measure to an accuracy of at least 200 nanometers (possibly much more accurate), so you could perform this trick using a rod about 70 meters long, assuming you could both read and write with that precision.

And if that rod was only a couple dozen nanometers thick, you could roll it up into a disk and you’d have a rough equivalent of a modern hard drive. (Although of course hard drives don’t store data as a single proportional mark, but you get the idea.)


#8

You know, these dudes have invented FTL travel, but they haven’t invented multiple digit numbers? I do not think I would volunteer to ride in their ships.


#9

Yeah, this one is great. It sounds so logical, it’s pretty tricky to see where the flaw in the logic is.


#10

Wow, I had totally forgotten these existed, but seeing those illustrations has brought me right back to being a kid and reading these!


#11

I love “Aha! Insight” and still have the beat-up copy I had as a kid. However there was one puzzle from “Match Games” (pg. 46) that I could never solve:


#12

The solution is terrible. There’s something very specific about that layout that’s a clue.


#13

I’ll be damned. I’ll just have to move on to grousing about the fact that the number is obviously already stored in his pocket computer…


#14

yeah that’s the issue, in simple arithmetic it’s:
(30/2) + (30/3) = 25
(60/5) * 2 = 24


#15

Which is to say it’s illustrating the importance of order of operations.


#16

Oh dear…got it now. Thanks 4 the hint…


#17

Encoding 3 digits per character: a-z as 001 - 026, A-Z as 101 - 126, space 200, etc
E (105) n (013) c (003) y (025) c (003) l (012) o (015) p (016) e (005) d (004) i (009) a (001)…
1.050 130 030 250 030 120 150 16…

At 10 nanometers you have “Enc”

At 10 femtometer (the size of the nucleus of a gold atom) you have “Encyc”

At the 10^-36 m ~ Planck length (the smallest unit of distance that makes sense in a quantum universe you have “Encyclopedia”


#18

They seem specially amazing for people with no grasp of arithmetic. The shop manager should probably go work for Burger King.


#19

on a similar note:

Even with human technology we can easily fit 300,000 physically depicted words in 0.01 square inch. (1)

The Encyclopedia Britannica has approximately 383333333 words. (2)

That means we could write the entire thing out in hebrew with 0.095 sq miles of surface area.
A totally different type of solution then described, and meaningless info so…
you are welcome! :stuck_out_tongue_winking_eye: oi vey! but i kid because this isn’t even the best example…

…and that isn’t even our smallest physical writing. IBM wrote their initials using 36 atoms. [3]

…and that isn’t even our smallest physical writing. Stanford wrote SU [4] using sub atomic particles. [5]

[quote]Finally, good news in the world of downsizing: Stanford University physicists have broken the historic record for small writing, opening a new door to computing’s future.

Their two letters - an “S” and a “U,” in honour of their employer - are so tiny that if used to print out the 32-volume set of Encyclopaedia Britannica, 2,000 times, the contents would fit on the head of a pin.[/quote]
which means we could write the entire thing out in English 2000 times on the head of a pin. The mark on the rod could contain the entire text and not even be big enough for most people to see.

it isn’t the size of the rod, it is how you use it to store information…or so i’ve been told.


#20

Is the answer: Just one match?
If it were me I’d move the one on the right out just a smidgen to create a small square in-between the matches…

Although I agree with @daneel that the solution i propose it terrible if it is the correct one.