Questions tagged [weighing]
A puzzle that is centered around weighings and balances.
200 questions
1 vote
2 answers
223 views
If it takes n weighings to identify the fake coin among k coins, then n+1 weighings will be required to identify the fake coin among 3k+3 coins
I was trying to solve the following puzzle: "We are given 12 coins. 11 of them are genuine and 1 is fake. All of the genuine coins weigh the same. The fake coin is either lighter or heavier than ...
- 7,575
5 votes
1 answer
461 views
Second-lightest coin from 30 with a 5-way balance
The following problem is lightly adapted from AoPS. You have 30 coins of identical appearance but distinct weights. You have only a balance that can rank exactly 5 coins from lightest to heaviest. ...
- 10.5k
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
8 votes
1 answer
380 views
Coins in Pockets 3 - Cough Up!
A follow-up to Coins in Pockets 2. Differences to that puzzle in bold. The strategy will probably be based on the solution to that previous puzzle - you might want to try it out first (or just focus ...
- 2,541
11 votes
1 answer
309 views
Coins in Pockets 2
This is a follow-up to Coins in Pockets Again, N persons are sitting around a camp fire. They have a total of C coins in their pockets (each person having an integer amount of coins), with C < N/2. ...
- 2,541
2 votes
0 answers
128 views
Guidance on Solving an Weighing Problem [closed]
You are given 3 bags of metal screws, with an equal number of screws in each bag. You do not know the number of screws in each bag. One of the bags has screws with a different weight than the rest. ...
3 votes
3 answers
175 views
Yet another balance problem
I fear it might not meet all requirements, but it is April, 1st... Published in the Journal de Genève in mid 80's, shortly before it ceased to exist.
- 1,053
12 votes
3 answers
2k views
Two Counterfeit Coins and a Balance
You have N coins, where N ≥ 5, and you know that exactly two of the coins are counterfeit and the rest are genuine. The genuine coins each weigh some amount w1 and the counterfeit coins each weigh ...
- 121
5 votes
1 answer
245 views
Weigh 15 boxes with a digital scale, but you can’t understand the number system
This puzzle is inspired by the puzzle 14 coins problem but you can't understand the scale. In this weighing puzzle, you have 15 boxes, each one weighing 1, 2, 3, and so on until 15 arbitrary units....
- 2,012
0 votes
2 answers
289 views
Weighing Coins -- a Different Approach
This is a question of my own devising. You have a double pan scale which will tell you whether 2 coins or 2 groups of coins weigh the same or whether one side is heavier than the other side. You have ...
- 846
0 votes
2 answers
1k views
6 balls, one is either heavier or lighter, find the odd ball in minimum weighings [duplicate]
You have 6 balls, of which one is either heavier or lighter, and you do not know which of the two situations it is. The other 5 balls all weigh the same. You have a balance scale. What is the minimum ...
- 7,575
5 votes
2 answers
344 views
Balls of different weights: how few balls can there be?
This puzzle was inspired by the one in this posting by Hemant Agarwal. There are n balls. Their weights are distinct positive integers which sum to W. The balls have the property that, if any one of ...
- 9,049
5 votes
7 answers
1k views
Prove that all 101 balls have the same weight
In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be divided into two groups of 50 balls each with the total ...
- 7,575
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
11 votes
3 answers
2k views
Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance
To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
