Questions tagged [weighing]
A puzzle that is centered around weighings and balances.
181
questions
4
votes
1
answer
770
views
Minimum number of turns
You have 64 identical-looking boxes numbered from 1 to 64, each weighing a distinct amount. On a turn, you can tell your friend two numbers between 1 and 64, and she will tell you which of the ...
- 76k
8
votes
5
answers
593
views
Minimum K for detecting fake pearls in one weighing
There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and any number ...
- 1,141
6
votes
2
answers
247
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 ...
- 8,010
5
votes
1
answer
227
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 ...
- 10.1k
1
vote
1
answer
135
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 ...
- 1
10
votes
3
answers
577
views
12 coins problem but you can't understand the scale
You have 12 coins 11 are real, one is fake but you don't know if it is lighter or heavier.
You have a scale that gives you output but you don't understand it (let's say it is written in a foreign ...
- 3,333
1
vote
1
answer
118
views
Centridipity problem
Two objects are fixed inside a moving car by strings so that they can both move freely.
The car's windows are closed.
A wind chime is suspended from the roof.
A helium balloon is tethered to the ...
- 578
3
votes
1
answer
245
views
Finding the median mass: is there a general solution for 2n + 1 objects?
Assume we have a two-pan balance. We are given a set of 2n + 1 coins which by condition all have different masses. Our task is to find the median coin, i. e. the coin that weighs more than any of n ...
- 76k
13
votes
7
answers
3k
views
Using a balance scale the minimum number of times, find the median weight person
There are 15 person with different weights.
What is the least number of tries required to find the middle (median) weight person? How?
The only tools you have is your brain and a balance scale with ...
- 26.3k
7
votes
3
answers
380
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 ...
- 8,010
0
votes
2
answers
158
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 ...
- 843
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 ...
- 1,188
23
votes
5
answers
35k
views
What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale by placing a certain combination of these weights onto ...
- 141
4
votes
2
answers
598
views
5 weights on modified balance scale
This question is follow up version of What's the fewest weights you need to balance any weight from 0,5 to 40 pounds, on a modified balance scale
with one arm twice as long as the other.
&...
- 1
0
votes
1
answer
463
views
Nine lemons, find the one that is different [duplicate]
You have 9 lemons, which all look exactly same. Same height, same color... There is no visible difference between any of them.
All lemons weigh the same amount, except for one, which weighs a little ...
- 134k
-1
votes
1
answer
161
views
Coin weighing - heaviest or lightest
I have 6 coins
Each coin has different weight
I can weigh as many coins at a time on a scale (for example I can weigh 3 vs 2)
I want to determine which coin is second heaviest or second lightest in ...
- 6,996
3
votes
2
answers
257
views
Ball weighing - second heaviest
Let's say we have 6 balls, where all of them have different weight.
Find and describe the least weighings you need on scales to find second lightest ball and second heaviest ball.
- 6,526
6
votes
3
answers
647
views
More Genuine and Fake Coins
I have 36 identical coins of which four, all weighing the same, are known to be fake. Fake coins are either all heavier than genuine coins, or all lighter.
At most how many weighings on a balance ...
- 8,010
0
votes
1
answer
202
views
General Fake Coin: k fake coins out of n coins
Considering a general fake coin problem. There are $n$ coins in total and $k$ of them are fake. Fake coins are lighter than the normal ones. You only have a balance to compare two groups of coins (no ...
- 1
3
votes
2
answers
2k
views
12 Coins 3 weighings generalization [duplicate]
I know the famous 12 coin, 3 weighings problem has been asked a few times already. And I saw at least one solution which can be adapted to this problem. Here's a generalisation (one of the many ...
- 27.9k
2
votes
1
answer
342
views
Generalization of twelve balls and scale problem
This problem is a generalization of Twelve balls and a scale problem. So I can solve and understand how things are going if we have 12 balls or 9 balls but how do I generalize? If say we have $3^n$ ...
CommunityBot
- 1
8
votes
1
answer
225
views
13 scales and a ... fake scale
You are given 14(*) scales that look and feel identical.
The scales are 2-pan scales. When you put stuff on each pan, the scale indicates whether both sides balance, and if not, which side is ...
- 26.8k
70
votes
7
answers
129k
views
Twelve balls and a scale
You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...
- 17.5k
15
votes
2
answers
3k
views
Why are all numbers from 1 to 2N covered by weights with powers of 3?
This is from What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Suppose you want to create a set of weights so that any object with an integer weight from 1 to N pounds ...
- 145k
5
votes
2
answers
236
views
Need Thorough Explanation of Coin Weighing Puzzle Solution
One of the coolest things I've seen on Puzzling is this puzzle, and especially the solution in 7 static weighings posted by Julian Rosen.
I have revisited that solution many times over the years, ...
- 2,976
7
votes
1
answer
251
views
Finding the weights of 3 coins
I have 9 coins; 3 coins each of 3 denominations.
Coins of the same denomination all weigh the same.
Each coin weighs an exact whole number of grams, and at most 9 grams.
I can weigh any subset of my ...
- 19.1k
4
votes
3
answers
7k
views
3 bags of coins, find which bag contains fake coins, doing only 1 weighing
Probably a very easy puzzle for you guys; my point is more a mathematical one.
FYI, it was shown in an episode of Columbo.
You have 3 bags of coins. Each bag contains 50 identical coins. Two bags ...
32
votes
5
answers
3k
views
Weigh a scale with itself
Using nothing but a pocket scale and a flat surface such as a countertop, find the total mass of the scale, including the attached metal plate and the plastic tray/cover (left).
Details about the ...
- 26.8k
2
votes
2
answers
285
views
19 balls and a scale [duplicate]
You are given 19 identical-looking balls and a two-sided scale. One of the balls is different, either lighter or heavier than the others. Using 4 weighings of the scale, how can you determine which ...
- 2,818
5
votes
2
answers
668
views
Gold, silver and bronze in the balance
Equivalent to finding three heaviest coins in order of weight,
on a balance that holds one coin on each side.
(Simplified, with some Wikipedia references corrected, from the original puzzle.
The ...
- 10.1k
15
votes
7
answers
4k
views
Twelve balls on a scale, where one ball is lighter and another is heavier
Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
- 229
5
votes
2
answers
926
views
Maximum number of masses you can weigh given 3 weights
The puzzle is as follows:
Assume that you have a two pan scale and three weights, one of 1 pound, the other 3 pounds and the last one 9 pounds. How many objects of different weights can you weigh at ...
- 50.8k
9
votes
5
answers
493
views
Breaking Balance (Part A)
If we assume the classic balance puzzle (Twelve balls and a scale) is phrased like this:
You have 12 coins that are identical except for one counterfeit that is heavier or lighter. Can you use a ...
- 10.1k
4
votes
1
answer
348
views
How to Balance?
You are given a scale which has 4kg and 2kg stones on the left side and an 8kg stone on the right side of the scale. You have an additional 1kg. How will you balance the scale?
- 39.2k
4
votes
1
answer
158
views
Identify heavier weights
[This is from one of my friends, a year ago]
We have 6 weights: 2 red, 2 black, 2 blue. Of each color, there is one that's 100g and one that's 101g. How can you identify which ones are 101g, in two ...
- 10.1k
11
votes
5
answers
2k
views
2 fake coins from a pile of 30 coins
You need to find two fake coins from a pile of 30 coins. You know that a fake coin has a different weight to a real coin, but you don't know whether it is lighter or heavier. You also know that all ...
- 10.1k
7
votes
4
answers
2k
views
How can you get 13 pounds of coffee by using all three weights each trial?
The puzzle is as follows [with minor copy edits for grammar]:
A merchant has a kiosk nearby our market. He has a sack of 52 pounds of coffee to sell. Assuming that he only uses a two pan scale and ...
7
votes
3
answers
436
views
Proving by weighting
Here is the puzzle:
Alice and Bob leave in a world where all diamonds are divided into 2 types: Light and Heavy. All diamonds look exactly the same. All light diamonds weight exactly the same, all ...
- 2,976
-3
votes
1
answer
103
views
Minimize cuts to an object to obtain weights which can be used to measure 1-40kg
The problem is as follows:
Rick has a small store and a two pan scale which allows him to weight the coffee he sells. Certain day he forgotten the weights that he uses in his truck, however in his ...
- 5,024
0
votes
1
answer
86
views
How can you use a two pan scale to find which coin is counterfeited? [duplicate]
The puzzle is as follows:
Detective Mike has four bags with 100 coins of one cent each. All of these coins have the weight with the exception of one coin which weighs a little less than the rest ...
- 4,274
11
votes
6
answers
16k
views
1 Fake Coin among N Amount of coins
You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale.
You are asked to find the fake coin in totally 5 times weighing on the Pan ...
2
votes
3
answers
440
views
Two of 18 coins are counterfeit
There are $n=18$ coins, and we know exactly $2$ of them are counterfeit. All counterfeit coins differ from normal coins in weight, but otherwise their weight is not known. They can be heavier or ...
- 10.1k
4
votes
2
answers
205
views
⌈3n/2⌉−2 weighings are required to find the lightest and the heaviest coin among n coins. Prove/disprove this
We are given n coins, all of which have a different weight. Prove/disprove that ⌈3n/2⌉−2 weighings are required to find the heaviest and the lightest coins among them using a 2 pan balance scale. You ...
- 2,818
10
votes
1
answer
1k
views
Is a fake coin lighter or heavier? [closed]
There are 16 coins, 3 of which are slightly heavier or lighter than the others. The counterfeit coins have the same weight but it is not known whether they are heavier or lighter than the genuine ones....
- 341
8
votes
2
answers
320
views
Another coin weighing puzzle, now including shifty coins!
You are, as you have been many times before, in some place that has a balance scale and 12 coins.
11 are all "normal" and stay normal, but one of these coins, however, is shifty -- as soon ...
- 2,963
3
votes
1
answer
216
views
Fewest number of weighings to check if coins are correctly labelled
This is inspired by the following question over at Computer Science Stack Exchange: Information-theoretic limits for a weighing puzzle
You are given 11 coins with labels 1, 2, 3, ... up to 11. You ...
- 141
3
votes
4
answers
354
views
Given pairs of weights find individual values
The problem is as follows:
A kid has five marbles. These marbles have different weights and the
child weighs them in pairs in all possible ways. He records the
weights in his notebook. These are the ...
- 8,010
2
votes
3
answers
122
views
Find the mass of a specific weight given information about other groups
The problem is as follows:
Vincent has 19 different calibrated weights whose weights are 1g, 2g,
3g, and so on up to 19g. Nine of them are made from steel,
nine are made from brass, and the remaining ...
- 11.6k
14
votes
6
answers
2k
views
Radioactive Rods
You have 8 identical looking rods, 2 of which are radioactive, though you don't know which. You also have a box which can test for radioactivity, which can hold any number of rods. After the test, the ...
- 1,770
23
votes
2
answers
12k
views
Coin weighing problem
You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision.
You know that all stacks of coins are made from gold, weighing 10 grams per ...
- 5,112