# Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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199 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, ...
117 views

### Balance Puzzle Find at most 2 counterfeit coins out of anywhere from >=3 # of coins

2 fake coins from a pile of 30 coins The real coins all weigh the same, and the fake coins weigh the same. The fake coins weigh less than the real coins. The difference in the one I am trying to solve ...
222 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 ...
370 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 ...
337 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?
96 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 ...
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 ...
580 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 ...
83 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 ...
426 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 ...
155 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 ...
147 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 ...
956 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....
311 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 ...
206 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 ...
119 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 ...
177 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 ...
271 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 ...
208 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 ...
1 vote
74 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. ...
826 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. ...
2k 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 ...
237 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 ...
454 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 ...
160 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 ...
268 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 ...
211 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 ...
401 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 ...
890 views

### Unbalanced weight of boxes

You are given a traditional balance scale with two pans (no reading) and 6 boxes with the following properties: 1) the weight of each box is a positive integer number 2) if you put any number of boxes ...
305 views

### How heavy each of these 7 creatures weights?

I was thinking about creating some riddle for TED-ED and somehow I came up some math riddle something like that: "A group of seven creatures weights together 1000 kg, the largest one and second ...
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 ...
4k views

### Are all balls the same weight?

There are 10 balls which come in two possible weights. Using a balance scale at most 3 times, determine whether all the balls are the same weight or not. Notes: I got this riddle from this ...
311 views

### 12 Distinct Weights' Sorting

There are 12 balls with all different weights. You want to sort these balls by weight. You have a friend who will help you with the ordering process. In each step, you give any 4 balls to your friend ...
606 views

### Sorting marbles based on weightings

You have 50 marbles which look all the same. However, 25 marbles have weight l and the other 25 marbles weight h with l < h. A person creates two piles and claims he has sorted all 50 marbles by ...
380 views

### Another coin weighing puzzle. But this is simple!

There are many coin weighing puzzles. So a general attribution to all of them. (And I will fully understand if you completely ignore this one). Hope this is not a duplicate. But I think this is a ...
42 views

### Using a balanced scale find the minimum and maximum weight of items [duplicate]

There are 1567 items with different weights. The goal is to find the item that has the maximum weight out of the 1567 and the item that has the minimum weight out of the 1567. For this you are allowed ...
4k 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 ...
1k 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 ...
1k views

### 30 fake coins out of 99 coins v2

Follow up question to my other question, but totally different methodology required. You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect ...
290 views

### The scales never lie (oh yes they do!)

There are $10$ coins, one of which is a fake, and weighs either more or less than the others - you don't know which. There are two sets of scales - one tells the truth, the other lies (always says ...
134 views

### Distribution of Work

The Leadman was instructed that on each floor level of the building under construction, there shall be two workers assigned to do some job. There are seven workers on the ground floor and five workers ...
285 views

### 12 balls 1 scale with 4 groups

So, we all know the famous 12 balls 1 scale riddle. It has been here repeated many times, however, the provided solutions always start with splitting the twelve balls into three groups of four. This ...
363 views

### The Tripan Balance

The tripan balance is used for comparing different weights. For example, when the pans carries 7 balls,5 balls and one is empty. The heaviest tilt to lowest level while the empty pan is at the highest ...
1 vote
316 views

### Minimize sum of guesses to win lottery

Ten boxes are given with $a_1,a_2,a_3,a_4,a_5 ......a_{10}$ number of balls in them respectively .These boxes are randomly ordered but $a_1,a_2 .....a_{10}$ is told.We can arbitrary select a box and ... 487 views

### Find the counterfeit coin

We are given ten stacks of three coins. All the three coins in one of the stacks are counterfeit. A true coin weights a whole number of grams. A false coin differs in weight from a true coin by less ...
954 views

### 10 coins, 3 of them are fake

Inspired by some great weighing puzzles here (This being one of my favorites), I just made another weighing puzzle - I'm not quite sure how difficult or easy this one is. You are given 10 coins, 7 of ...
1k views

### Find a stone which is not the lightest one [closed]

I've gotten this riddle and have been struggling with solving it: Suppose you have 20 stones which have different weights [0 ... n] . You have no way of measuring the weight of any stone individually,...
653 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 ...
This puzzle is based on a competitive programming problem in SG NOI 2019. Let's assume there are $100$ balls with some labels (e.g. with $100$ different marks on them) having different weights of ...
There are $n=4$ coins and we know exactly $2$ of them are counterfeit. In $2$ weighings, how can we find which of the four coins are the counterfeit ones? Assumptions: the counterfeit coins look ... 