# Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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### 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 ...
13k 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 ...
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13k views

### N balls and a scale

The question of twelve balls and a scale is probably the best-known example of the "find the ball of a different weight" problem. But does it generalize? Is there a general way to find a weighing ...
36k 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 ...
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 ...
• 30.3k
438 views

### Shortest number of attempts to solve this issue [duplicate]

There are 9 identical balls but only one of them has a higher weight. You are also given a weight balance. How many attempts would you require to identify the ball with the extra weight and how?
• 31
554 views

### A balance with three pans, detecting the lightest pan (find the one lighter ball)

The following puzzle was told to me by a friend, Markus Götz, who put it online here: Deviating Ball Puzzles (pdf). After some searching, I did not find this puzzle anywhere else online. The only ...
2k views

### A balance with three pans, detecting the lightest pan (find the two heavier balls)

This is a continuation of the question A balance with three pans, detecting the lightest pan (find the one heavier ball). It was told to me by a friend, Markus Götz, who put it online here: Deviating ...
1.4m views

### Brooklyn 99 riddle: Weighing Islanders [duplicate]

This one comes from this week's Brooklyn Nine-Nine episode! There is an island with 12 islanders. All of the islanders individually weigh exactly the same amount, except for one, who either weighs ...
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384 views

### A balance with three pans, detecting the lightest pan (find the one heavier ball)

This is a continuation of the question A balance with three pans, detecting the lightest pan (find the one lighter ball). It was told to me by a friend, Markus Götz, who put it online here: Deviating ...
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 ...
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1k views

### Derivative of the coin weight problem [duplicate]

Most people are familiar with the following problem: A well-known example has nine (or fewer) items, say coins (or balls), that are identical in weight save for one, which in this example is lighter ...
3k views

### Trapped in my Cellar

I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
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2k views

### 30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
• 30.3k
1 vote
448 views

### The n coins and the scales [duplicate]

The other day I was reading a puzzle book and found this classic: There are 9 coins on the table, but one of them is fake and weighs slightly less (or more, doesn't matter). How many measures do you ...
4k views

### Coin weighing with a single weighing device

You have 12 coins which each weigh either 20 grams or 10 grams. Each is labelled from 1 to 12 so you can tell the coins apart. You have one weighing device as well. At each turn you can put as many ...
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3k views

### 15 Distinct Weights' Sorting

There are $15$ balls. Each of them has a different weight. You want to sort them according to their weights. You have a friend who will help you with his scale to do this. At each weighing process, ...
• 151
4k views

### 68 coins with 100 weighings

You have 68 coins of different weights. Using only a balance scale and the coins themselves, find the heaviest and lightest of the coins with only 100 comparisons. This puzzle is adapted from The ...
• 253
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 ...
2k views

### Find two coins using a balance scale

You are given 20 identical coins. 18 of those coins have a weight of 10g each, 1 coin has 9g and 1 coin has 11g. You are given a traditional balance scale with two pans (no reading). What is the ...
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1k views

### Bag of gold coins weighing with a digital scale

We are given 100 bags, each with 200 coins. All but one of the bags are filled with identical gold coins, but the other bag contains fake coins. The fakes all weigh the same as each other, but weigh ...
• 81
586 views

### Balancing all but one weight

You have an odd number of tokens whose weights are known whole numbers, and they don't all have the same weight. Show that there's a token you can remove so that the remaining tokens can't be split ...
• 27k
1 vote
2k views

### The heaviest orange [duplicate]

You have a basket of 9 oranges, 8 of the oranges have the same weight and 1 is heavier than the others. All the oranges looks and feels the same. You have a scale but you are allowed to use it only 2 ...
• 113
4k views

### Thirty genuine and seventy fake coins

In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions: All genuine coins have the same ...
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2k views

### Unknown weight of four identical objects

Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you ...
811 views

### A Dozen Golden Eggs

Twelve golden eggs are arranged on the shelf according to shell thickness with weight tags in ounces. You've been told that two of the eggs were swapped by some culprit! You must put them back again ...
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1k views

### Fifty-two genuine and two fake coins

In the country Borgonia, there are only two types of coins: genuine ones and fake ones. All genuine coins have the same weight, and all fake coins have the same weight. The weight of a genuine coin is ...
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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 ...
• 5,756
914 views

### Lots of Gold Stacks and a Balance Scale

You are given X amount of stacks of golden coins, each stack consisting of ten (10) golden coins and a digital balance scale with perfect precision that shows how much difference between weights you ...
• 30.3k
627 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 ...
• 111
445 views

### Weighing in 89 different ways

On the table, there is a balance with two pans together with ten weights ofrespectively 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512 grams. Cosmo takes a coin out of his pocket, shows it to Fredo and ...
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4k views

### Four coins (plus one) and a balance

Someone gives you 4 apparently identical golden coins. You know that among them there could be exactly one fake coin, and that a fake coin hasn't the same weight of a golden one. In your pocket you ...
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1k views

### Breaking Balance (Part C)

For a starting number of otherwise identical coins there are among them TWO IDENTICAL counterfeit coins which are either heavier or lighter than the rest. Using a three-pan balance (described in ...
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3k views

### What's the fewest weights you need to balance any weight from 0,5 to 40 pounds, on a modified balance scale

One arm of a weighing scale is twice as long as the other. Suppose you want to create a set of weights so that any object weight from 0.5 and its multiples up to 40 pounds can be exactly balanced ...
• 17.9k
713 views

### The Ebbozonian coin weighing puzzle

In the country of Ebbozonia, there are only two type of coins: light coins and heavy coins. The weights of these coins satisfy the following properties: All light coins have the same weight $L$. All ...
• 45.6k
701 views

On the table, there is a balance with two pans. The display on the balance tells the difference between the weight in the left ban and the weight in the right pan (measured in gram). There are also $... • 45.6k 7 votes 11 answers 4k views ### 121 coins and a balance Inspired by this puzzle... You have$121$apparently identical gold coins. At most one of these is fake, and weighs a different amount than a genuine coin. In front of you is balance with two pans. ... • 32.4k 6 votes 3 answers 435 views ### Finding both fake coins in a set of$5$There are$5$rupees on Arnav's table. He knows that exactly$2$of the rupees are counterfeit. One of these$2$coins is lighter than a normal (non-counterfeit) rupee, and one of these$2$coins is ... • 115 5 votes 2 answers 276 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 ... • 2,939 4 votes 2 answers 605 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. &... • 30.3k 4 votes 1 answer 562 views ### Are there basic weighing puzzles requiring adaptive strategies? Let us define a basic weighing puzzle as such: There are <number> identical balls, except one weighs <more/less/a different amount than the others> A balance scale may be used to weigh two ... • 22k 4 votes 1 answer 215 views ### A balance with three pans, detecting the lightest pan (find the one lighter/heavier ball, for a given number of balls) This is a continuation of the questions A balance with three pans, detecting the lightest pan (find the one lighter ball) and (find the one heavier ball). There, I asked for the maximum n given a ... 3 votes 1 answer 454 views ### Breaking Balance (Part C-minor: easy version!) Identical to Breaking Balance (Part C), except with two weighings. For a starting number of otherwise identical coins there are among them TWO IDENTICAL counterfeit coins which are either heavier ... • 5,158 3 votes 1 answer 590 views ###$N_{max}\$ balls in 3 weightings

This is a small generalization of well known 12 balls puzzle: You are given two-sided scale and some number of balls. All balls have the same weight but one. It is of a different weight, although ...
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1k views

### Find 2 heavy coins among 27 with a 3-pan balance

This is an extension of a previous three-pan balance puzzle. I give you a bag containing 27 coins, which look exactly the same. Among them are two fake coins. All genuine coins weigh the same. The ...
455 views

### Two heaps each with a heavy ball, and a 3-pan balance

The three-pan balance Imagine a balance with not two, but three pans. Weighings using the balance follow these rules: If there exists a pan that is lighter than each of the other two pans, then this ...
455 views

### Weigh eight balls and find the lighter one [duplicate]

There are similar puzzles but I think this one is different. You are given eight metal balls. You know one weighs less than the rest. You are given a balance scale. What is the smallest number of ...
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840 views

### Find the Different Sugar Cubes [duplicate]

There are 10 Boxes, each contains 1000 sugar cubes. The sugar cubes in 9 of the boxes are 10 grams each and the other box has 9 gram cubes. There is a digital scale that you can use it ONCE. (i.e. ...
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