# Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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### 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 ...
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 ...
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 ...
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 ...
1 vote
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 ...
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 ...
1 vote
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.   &...
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 ...
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 ...
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.
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 ...
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 ...
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 ...
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 $3^n$ ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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....
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 ...
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 ...
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 ...
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 ...