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
- 116k
32
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:
- 18.2k
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 ...
- 116k
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:
- 5,676
20
votes
Accepted
Simulating a biased coin with an unbiased one
Yes, you can do it like this:
Why does this work?
- 145k
16
votes
Accepted
Coin removal problem
The row of coins can be fully removed if it has the following property:
Proof:
Solving strategy:
- 50.3k
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 ...
- 4,081
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.
- 17.9k
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 ...
- 1,745
11
votes
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:
- 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 ...
- 126
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. ...
- 50.3k
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 ...
- 2,953
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, ...
- 2,071
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 ...
- 492
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:
- 5,653
7
votes
7
votes
Accepted
7
votes
Simulating an unbiased coin with a biased one
A straightforward answer (actually, a generalisation of loopywalt's answer):
Example:
- 11.3k
7
votes
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 ...
- 32k
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\...
- 7,428
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.
- 50.3k
6
votes
Accepted
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,...
- 229
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 ...
- 2,944
6
votes
Accepted
6
votes
Accepted
Twenty-four coins
Here's an algorithm that requires maximum 7 measurements (I believe):
Let's first set some terminology, note that each measurement of n coins can be one of 4 cases:
Case 0: All standard coins M = n.s
...
- 1,053
5
votes
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