Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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4 answers
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How many ways to iterate? [duplicate]

There are 9 coins, out of which one is odd, i.e. its weight is either less or more than that of the other 8 coins. How many iterations of weighing using a pan balance are required to find the odd coin ...
nrb's user avatar
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6 votes
1 answer
358 views

Maximize all weights

This question is related to What's the fewest weights you need to balance any weight from 1 to 40 pounds? You had 4 weights to balance any weight from $1$ to $40$ pounds which is answered previously ...
Oray's user avatar
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0 votes
4 answers
9k views

Which one is the poisoned pill? [duplicate]

One of my friends shared this picture to me, actually I don't know from where it came from but it seems interesting to solve. Please check below:
CR241's user avatar
  • 574
6 votes
6 answers
1k views

Not the Weight thing again!

John, a graduate student in US, walks into his apartment kitchen with his laptop. On the counter his roommate has left a note next to what looked like a door lock. The lock was a rectangular prism ...
DrD's user avatar
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6 votes
1 answer
172 views

There is a room full of balances which is in perfect balance

The 12 weights look identical and weigh 1kg,2kg,3kg......12kg.Each mark on the rod is 1m apart. Identify which weight is where and sum of marked weights
ULTIMATEGAMER07's user avatar
9 votes
9 answers
3k views

Faulty Weight Scales

You are in a room with 3 digital weight scales and a big book. The digital scales are small like the ones you see in small stores. They are identical in all aspects. They all have a READ button which ...
DrD's user avatar
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0 votes
0 answers
85 views

Analytical puzzle [duplicate]

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale....
Khushbu_sipl's user avatar
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 ...
Oray's user avatar
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19 votes
8 answers
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 ...
Oray's user avatar
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0 votes
2 answers
436 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 ...
Hashbrowns's user avatar
7 votes
1 answer
712 views

The different twins

The seesaw is filled with nine pairs of identical twins. All the kids weigh the same (e.g., they all weigh 100, but the actual numbers are irrelevant), except for one set of twins. They are still ...
TSLF's user avatar
  • 6,626
6 votes
7 answers
756 views

A Two Faced Coin

A stack of 12 coins that looks identical are to be tested for the unusual one which become slightly lighter on one face and slightly heavier on the other face. If it is weighed standing on its side, ...
TSLF's user avatar
  • 6,626
32 votes
14 answers
4k views

15 Balls Sorting

This is a variant of 15 Balls Weighing. You have 15 balls of 15 different weights, but the weights are so similar you can't tell them apart by feel. The balls are also identical by any other sense ...
user3294068's user avatar
  • 7,438
11 votes
5 answers
414 views

A Dozen Golden Eggs, Part 2

This is a variant of A Dozen Golden Eggs posted by TSLF, this time with the digital scale removed. You have twelve golden eggs arranged on the shelf according to shell thickness, with weight tags in ...
Rand al'Thor's user avatar
17 votes
1 answer
807 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 ...
TSLF's user avatar
  • 6,626
4 votes
2 answers
168 views

Selecting weights to minimize weighings

In this weighing problem objects of four different weighs are to be identified with four weighings with a balance scale. Now given that the four weights are all different, on one hand, there are $4!=...
celtschk's user avatar
  • 2,750
25 votes
2 answers
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 ...
Jackson murphy's user avatar
-2 votes
2 answers
426 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?
Sam's user avatar
  • 31
12 votes
2 answers
865 views

Determine your weight from 2 different answers from 2 weighting scales

You have 2 movable weighing scales. Their least count is 1 gram. You have tried both to find out your weight, but they give you different answers. You do not know whether both of them are ...
Jamal Senjaya's user avatar
15 votes
6 answers
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, ...
rasim's user avatar
  • 151
8 votes
2 answers
796 views

Lots of Gold Golden Coins and a Scale

Following my previous question: Lots of Gold Stacks and a Balance Scale You are given 10 stacks, each stack consisting of N golden 10g-coins and a digital scale with perfect precision that shows ...
Oray's user avatar
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8 votes
3 answers
2k views

Forty-six genuine and two fake coins

Inspired by this puzzle. In the country Dragonia, 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. It is ...
shoopi's user avatar
  • 2,625
13 votes
6 answers
896 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 ...
Oray's user avatar
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9 votes
3 answers
627 views

The King's New Accountant

The king of Ebonchester has just returned from his recent conquests of Baronshire and with him he brought four cart loads of plunder. However Baronshire is known for its lacklustre fiscal regulation, ...
Scoranio's user avatar
  • 704
8 votes
2 answers
554 views

Minimum number of tries to find the balance!

There are 8 distinct weights and a two-pan equal arm balance scale, and you know the weights' weight order: the lightest is numbered as 1 and the heaviest is numbered as 8 and the rest accordingly. ...
Oray's user avatar
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3 votes
1 answer
483 views

Another 2016 coins and a balance

This continues the puzzle "2016 coins and a balance". Again, there is a balance with two pans on the table. Again, the display on the balance tells the difference between the weight in the left ban ...
Gamow's user avatar
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7 votes
2 answers
691 views

2016 coins and a balance

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 $...
Gamow's user avatar
  • 45.4k
11 votes
4 answers
309 views

Rank the Fencers

There are five fencers. Each has a particular skill level, all of which are different. When two fencers duel, the one with the higher skill level always wins. How many duels do the fencers need to ...
Mike Earnest's user avatar
  • 32.1k
10 votes
5 answers
5k views

Using a balance to determine any weight with a set of weights weighing powers of 3

There is a scale with an object on the left-hand side, whose mass is given in some number of units. Predictably, the task is to balance the two sides. But there is a catch: You only have this peculiar ...
Jenny's user avatar
  • 201
10 votes
4 answers
1k views

212 weights of 1 gram

Fredo owns a balance with two pans and 212 weights, each of 1 gram. Fredo proudly announces to Cosmo that his weight system has the following stunning property: For every integer weight $W$ with $1\...
Gamow's user avatar
  • 45.4k
16 votes
4 answers
947 views

Weighing in 2015 different ways

This question was inspired by something I realized while thinking about @Gamow's Weighing in 89 different ways. You have a two-pan balance and $2015$ weights, with masses $1,2,4,\ldots, 2^{2014}$. ...
f'''s user avatar
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10 votes
2 answers
443 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 ...
Gamow's user avatar
  • 45.4k
5 votes
3 answers
921 views

A balance and twenty weights

Fredo owns a nice balance with two pans. He now wants to design a system of 20 integer weights $w_1,w_2,\ldots,w_{20}$ with the following properties: $1\le w_1\le w_2\le w_3\le\cdots\le w_{20}$ Any ...
Gamow's user avatar
  • 45.4k
6 votes
3 answers
783 views

Another Ebbozonian coin weighing puzzle

This puzzles continues "The Ebbozonian coin weighing puzzle" from last week. In the country of Ebbozonia, there are only two type of coins: light coins and heavy coins. The weights of these coins ...
Gamow's user avatar
  • 45.4k
8 votes
3 answers
700 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 ...
Gamow's user avatar
  • 45.4k
5 votes
1 answer
382 views

Find k defective balls out of n balls

There are $n$ balls out of which $k$ are defective, where $k<n/2$. All defective balls have the same weight $w$, and all non-defective balls have the same weight $v$ with $v<w$. Determine all ...
user avatar
1 vote
2 answers
3k views

Ball Weighing Riddle

A twist on the classic, "how many weighings to find the odd weight ball in 9 balls". Suppose there is n balls. There are two types of balls. One type weighs less than the other. In the set of balls ...
Johnxl's user avatar
  • 13
16 votes
5 answers
1k views

Evaporating coins

In the country of Dalgonia, there is only one type of fake coins and only one type of genuine coins. All genuine coins have the same weight. All fake coins have the same weight. Fake coins and ...
Gamow's user avatar
  • 45.4k
-1 votes
1 answer
232 views

Seven Spheres of Unequal Mass, a weighing problem with a twist

You have a scale that is remarkably sturdy, and there are seven spheres of unequal mass. No sphere has the same mass as any other. There is (almost) no limit to the mass of any sphere, but the most ...
Kingrames's user avatar
  • 2,697
36 votes
9 answers
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 ...
Gamow's user avatar
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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 ...
Dr Xorile's user avatar
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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 ...
Mike Earnest's user avatar
  • 32.1k
0 votes
1 answer
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 ...
Freddie's user avatar
-1 votes
1 answer
156 views

A pile of fakes [duplicate]

You're working in a bank and you've been given ten piles of coins. One of the piles, you've been told is a pile of fake coins. The real coins are 100g in weight, while the fake coins are just 90g. ...
Beta Decay's user avatar
0 votes
7 answers
11k views

Weighing an elephant [closed]

Here's another classic I couldn't find on the site: How can you determine the weight of an elephant without using a scale?
mmking's user avatar
  • 3,106
2 votes
4 answers
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 ...
Christian Semrau's user avatar
2 votes
3 answers
453 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 ...
Christian Semrau's user avatar
7 votes
1 answer
744 views

Find 2 heavy fakes among 11 coins on a 3-pan balance

I give you 11 coins, which look exactly the same. Among them are two fake coins. All genuine coins weigh the same. The fake coins are a little heavier than the genuine ones, and they may have a ...
Christian Semrau's user avatar
9 votes
2 answers
617 views

Six balls, six weighings

Six spheres, six weighings. If you grow impatient with the narrative, you can skip to the TL;DR, below. An engineer was walking across the street, on the way back from lunch, when bam, hit by a bus. ...
user3294068's user avatar
  • 7,438
4 votes
1 answer
214 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 ...
Christian Semrau's user avatar