Questions tagged [coins]
Puzzles involving the manipulation of coins as physical objects inside a set of rules.
45 questions
3 votes
1 answer
282 views
2 counterfeit out of 16 within 3 weighing
I face a question as follow from my friend. I wonder whether we can identify the location of counterfeits or just the number of coins lie between them. Given 16 identical coins in a row. There is ...
- 33
19 votes
7 answers
3k views
100 coins on a table
You have 100 coins enumerated on a table, with H heads and T=100-H tails. Your goal is to make all coins heads. You are blindfolded so you ask a friend to stand in front of the coins. At the beginning,...
- 965
18 votes
4 answers
3k views
Packing coins in a square frame
Show that there exists a square frame and a set of identical circular coins, such that the coins can be rigidly packed in the frame in more than one arrangement. Remarks: "Rigidly packed" ...
- 5,205
18 votes
2 answers
1k views
In a circular tray of radius 1, arrange coins of radius 1/2, 1/3, 1/4, 1/5 so that none of them can move independently
In a circular tray of radius $1$, arrange coins of radius $\frac12,\frac13,\frac14,\frac15$ - at least one of each, and no other kind of coin - so that none of them can move independently, i.e. if any ...
- 5,205
4 votes
0 answers
153 views
The Merchant's coin weighing [duplicate]
You're a merchant in the old medieval times, and a customer has come to you to buy something for 13 coins. You know him of course, like everyone in town, and you know he's a sketchy guy. Someone who ...
- 3,192
9 votes
1 answer
425 views
Communicate square on a 3-by-3 grid by flipping precisely one of 13 coins
A coin is placed on each of the $13$ squares in the following diagram: Each coin may be showing heads or tails arbitrarily. An adversary points to a square in the $3\times 3$ grid. You must ...
- 1,181
4 votes
1 answer
3k views
A puzzle about two coins of total value of 15 cents, one of which is not a nickel. Is it correct at all?
The puzzle: In my pocket, I have two US coins of total value of 15 cents. One of my coins is NOT a nickel. What are the coins? A mathematician told me that I was totally wrong when I posted my ...
- 615
8 votes
5 answers
3k views
Move a coin without touching it
There are three coins lying flat on a table, arranged in a straight line with their edges touching. Call the coins A, B, and C (B is in the middle). Here are the rules: You can touch and move only ...
- 7,213
1 vote
1 answer
158 views
The Coin Conundrum [closed]
You are a coin collector who recently acquired a set of rare antique coins. The set contains 14 coins - 12 are authentic but 2 are counterfeit. The real coins each weigh 1 oz, while the fakes each ...
5 votes
1 answer
330 views
14 coins problem but you can't understand the scale
The 12 coins 12 coins problem but you can't understand the scale asks for is not the maximum possible, therefor this follow-up question: You have a number of coins, one is fake but you don't know ...
- 11.4k
6 votes
2 answers
621 views
How many solutions to the twelve coins problem are there?
I was recently asked to solve the classic twelve coins balance problem: You are given twelve coins, eleven of which are equal in weight and one of which is either heavier or lighter than the other ...
- 163
7 votes
3 answers
549 views
How many weighings does it take to find out which of the 10 coins is fake using a digital scale
Lets say you have 10 coins, any number of which may be fake. You know how heavy the fake and real coins are, and you have a digital scale. (so you'll know exactly how many of the coins are fake.) How ...
- 194
0 votes
2 answers
292 views
How many times do you need to use the scales to find the fake coin [duplicate]
Let's imagine that you have ten large bags of coins - nine of them real, one of them fake. You don't know how much the fake coins or the real coins each weigh, but you know that they differ. If you ...
- 194
6 votes
4 answers
879 views
How to Divide 1,987 Gold Coins Among 40 Pirates?
There are 40 pirates, designated as P1, P2, ...... P40, respectively. They aim to divide 1,987 gold coins using a two-stage division scheme: In the first stage, P1 initially splits all the coins into ...
- 948
12 votes
6 answers
1k views
Twenty-four coins
I have twenty-four identical-looking coins, but two are fake and weigh possibly different from each other, though definitely different from the remaining genuine coins. I have a weighing scale and a ...
