42 votes
Accepted

68 coins with 100 weighings

It seems to me that there's a simpler solution than the one accepted above. Step 1: Step 2: Step 3: The point here is that
Gareth McCaughan's user avatar
34 votes
Accepted

Simulating an unbiased coin with a biased one

One possibility: This works because: EDIT: Inspired by @trolley813's answer here is a way to recycle the rejected entropy:
loopy walt's user avatar
  • 21.4k
28 votes

Coin Game with infinite paradox

OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less ...
Gareth McCaughan's user avatar
25 votes

68 coins with 100 weighings

I see, it took me too long to fininsh my drawing, but let me present it as additional material to sousben's answer:
A. P.'s user avatar
  • 5,948
21 votes
Accepted

Move a coin without touching it

ibanezplyr's user avatar
20 votes
Accepted

Simulating a biased coin with an unbiased one

Yes, you can do it like this: Why does this work?
Deusovi's user avatar
  • 146k
16 votes
Accepted

Coin removal problem

The row of coins can be fully removed if it has the following property: Proof: Solving strategy:
Jaap Scherphuis's user avatar
16 votes

Coin Game with infinite paradox

This gambling problem is the famous St. Petersburg paradox. It is a paradox because The one issue with this theoretical result is that it requires no upper limit on the possible winnings - if you ...
Nuclear Hoagie's user avatar
16 votes
Accepted

A puzzle about two coins of total value of 15 cents, one of which is not a nickel. Is it correct at all?

If the puzzle had said that neither coin was a nickel, a solution could have consisted of: But with the puzzle as actually posed, your answer was correct, and the person who responded to you was both ...
isaacg's user avatar
  • 6,944
14 votes
Accepted

How will Y lose the game?

Generalization. There are $K$ coins on the table and one player can pick as many as M coins at once.
Marius's user avatar
  • 18.1k
13 votes

How will Y lose the game?

Using winning/losing position analysis you can tell that the correct move is to take: You can work this out iteratively. If you have 1 coin and it is your turn you will obviously lose. Thus 1 is a ...
Chris's user avatar
  • 1,825
11 votes

Coin Game with infinite paradox

I would pay
Moacir's user avatar
  • 211
10 votes

68 coins with 100 weighings

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Then This makes a total of:
sousben's user avatar
  • 2,586
9 votes
Accepted

Five Men and Four Coins Puzzle

For my answer I'm considering the sides of the coin to either have a star or be blank for ease of writing. I also will write out the number for peoples name, and use the character for guesses to try ...
Alex Holder's user avatar
9 votes

Sand Castle Builder Glass Ceilings Puzzle

There are several physical versions of this puzzle: (Elephant) Spinout, by thinkfun: The Brain, by Mag-Nif: and the traditional Chinese Rings puzzle: The solution is based on the Binary Gray Code. ...
Jaap Scherphuis's user avatar
8 votes

Coin Game with infinite paradox

There are several nuances to this question. First of all, it asks how much you are willing to pay, not what price is fair. Second, you have to understand, that even if a game is fair, that does not ...
Amorydai's user avatar
  • 2,963
8 votes

Coin Game with infinite paradox

I would not pay anything. I would not play. I would encourage you to not play. Are you doing okay? I'm willing to help you out of you need help. I would offer you a hug. You are my best friend, ...
Ben Barden's user avatar
  • 2,081
8 votes
Accepted

12 coins problem but you can't understand the scale

This was quite a fun twist on weighing puzzles. The fact we don't know what the scale outputs mean requires us to, as part of our weighing procedure, decipher the scale's output. Luckily, we only need ...
Tez LaCoyle's user avatar
7 votes
Accepted

The Dollar Bill

One Dollar One dollar Which should look something like the following image:
Joel Harmon's user avatar
7 votes

Five Men and Four Coins Puzzle

The first toss is a star (*) or not (-). Mr Two immediately loses. The second flip can be either, so we have **, *-. -*, or --. Also on that flip, The third and fourth flip and To sum:
Kate Gregory's user avatar
  • 5,810
7 votes

How will Y lose the game?

X should pick up Because Examples:
indubitablee's user avatar
  • 2,019
7 votes

Simulating an unbiased coin with a biased one

A straightforward answer (actually, a generalisation of loopywalt's answer): Example:
trolley813's user avatar
  • 11.3k
7 votes

Simulating a biased coin with an unbiased one

This works because
hdsdv's user avatar
  • 5,190
6 votes

Bag of gold coins weighing with a digital scale

Numbering the bags from 1 to 100, here is the weighing strategy: To deduce the true bag, let...   $t$ be the weight of a true coin.   $\delta$ be the difference between weight of a fake ...
Mike Earnest's user avatar
  • 32.4k
6 votes

Counterfeit Detector

It is possible, but only if you test 5 coins the first time. The difficulty is that, if all the tests up to a certain point have answered No, and there are $k$ coins remaining, then there are $k\...
user3294068's user avatar
  • 7,498
6 votes
Accepted

Riffing off of Dudeney

First puzzle in 4 moves: Second puzzle in 5 moves: The way I solved these is I do not know if these are optimal. I would not be surprised if shorter solutions are possible.
Jaap Scherphuis's user avatar
6 votes
Accepted

Finding both fake coins in a set of $5$

SDwarfs's user avatar
  • 211
6 votes

Coin Game with infinite paradox

$16, Consider what else we know: You are my best friend The currency you're using is US dollars You own a home (namely the one next to mine) What do these things imply? Because I'm your best friend,...
Mathaddict's user avatar
6 votes

12 coins problem but you can't understand the scale

Once you can identify which symbol means "equal", this reduces to the original problem. That is because if you follow a valid strategy assuming that A means "left heavier" and B ...
Especially Lime's user avatar
6 votes
Accepted

Sand Castle Builder Glass Ceilings Puzzle

N=1 N=2 N=3 N=4 N = 5 N = 6 Formula for any N:
xyldke's user avatar
  • 1,773

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