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# Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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3 votes
2 answers
195 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 ...
• 8,672
0 votes
3 answers
340 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 ...
• 3,157
4 votes
0 answers
137 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 ...
• 2,653
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! ...
• 12.1k
16 votes
2 answers
2k views

### Find the heaviest and the second heaviest coins

Each of 32 coins has a different weight. In 35 weighings on a standard balance, find the heaviest and the second heaviest coins. Clarification: Before you start to identify the heaviest and second ...
• 12.1k
9 votes
1 answer
317 views

### Designing a four-pan scale

You are an ancient merchant, and you need to weigh out many different items of many different weights. To do so, you'll design a scale to weigh objects. Unlike a standard scale, your scale will have ...
• 7,148
8 votes
2 answers
538 views

### Seven genuine and two fake coins

Seven genuine coins have the same weight. Two counterfeit coins also have the same weight. A counterfeit coin is heavier than a genuine coin. Identify the fake coins using a standard balance at most ...
• 12.1k
5 votes
1 answer
813 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 ...
• 336
9 votes
5 answers
607 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 ...
• 938
1 vote
1 answer
141 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 ...
5 votes
1 answer
243 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 ...
• 9,278
6 votes
2 answers
308 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 ...
• 163
1 vote
1 answer
128 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 ...
• 14.5k
3 votes
1 answer
254 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 ...
• 595
7 votes
3 answers
396 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 ...
• 194
0 votes
2 answers
206 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 ...
• 194
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 votes
1 answer
169 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 ...
• 263
3 votes
2 answers
296 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.
• 263
6 votes
3 answers
1k 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 ...
0 votes
1 answer
223 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 ...
8 votes
1 answer
234 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 ...
• 30.6k
2 votes
1 answer
550 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 $3^n$ ...
• 635
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 ...
• 635
5 votes
2 answers
275 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, ...
• 19.4k
7 votes
1 answer
260 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 ...
• 53.7k
10 votes
3 answers
638 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
4 votes
1 answer
351 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?
-3 votes
1 answer
109 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 ...
• 1,565
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 ...
• 1,565
5 votes
2 answers
1k 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 ...
• 1,565
0 votes
1 answer
89 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 ...
• 1,565
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 ...
• 16.3k
5 votes
2 answers
296 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 ...
• 3,157
4 votes
1 answer
159 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 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....
• 259
8 votes
2 answers
324 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 ...
• 795
3 votes
1 answer
220 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
2 votes
3 answers
123 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 ...
• 1,565
3 votes
4 answers
472 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 ...
• 1,565
2 votes
2 answers
295 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 ...
• 29
5 votes
1 answer
343 views

### Interesting Puzzle About Indian And Brazilian Marbles [duplicate]

There are 8 boxes each containing 8 marbles. There are two kinds of marbles – Brazilian kind and Indian kind. Each marble of the Brazilian kind weighs 12 units and each marble of the Indian kind ...
• 51
1 vote
0 answers
81 views

### Island Riddle. - How would you approach this and what is your mentality? [duplicate]

There are 12 people on an island. 11 of the 12 people weigh the exact same. However one of them weighs different(more or less you don't know). You have a seesaw. You can only use the seesaw 3 times. ...
• 69
4 votes
2 answers
1k views

### How to solve Centrifuge problem

I have a balancing problem which I am not sure if I understand completely correct. Centrifuge has 36 holes. If in a hole only one test tube can be placed and all the test tubes are with equal weight. ...
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 ...
• 423
4 votes
4 answers
251 views

### Weighing half-balls

A bearing factory cuts four solid steel balls into halves by rolling them through the vertical laser and then drops into a collecting bin. The eight half-balls looks identical but due to rail ...
• 6,656
10 votes
1 answer
682 views

### Simplified triple beam scale

What could possibly be simpler than a triple beam scale? (Ohaus Corp.) A simplified triple beam scale, of course: Just one identically spaced pair of notches on each beam, allowing 2 possible ...
• 21.9k
3 votes
1 answer
198 views

### 4 balls and a balance scale

What's the least amount of weighings you'd need to be able to successfully determine the weights of 4 balls weighing 1, 2, 3 and 4 kilograms, using a balance scale (counting the worst scenario)? Any ...
12 votes
3 answers
304 views

### The Chess Moments

The chessboard was well balanced on the mid horizontal by some fulcrum. Black and white pieces were carefully placed on such board for equilibrium. Because the wooden pieces weights vary, their ...
• 6,656
3 votes
3 answers
217 views

### Does there exist a way to find the least number of trials when a certain weight is requested?

I'm not very sure how to tackle this sort of problem: It is as follows: At a groceries store there is a two pan scale and two weighs which are of $250\,g$ and the other of $500\,g$. It is known ...
• 1,565