Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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3
votes
1answer
295 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
1answer
79 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 ...
7
votes
4answers
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 ...
4
votes
2answers
378 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. In only one weighing trial, how many objects of ...
0
votes
1answer
62 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 ...
6
votes
3answers
405 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 ...
4
votes
2answers
136 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
votes
1answer
135 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
1answer
850 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....
7
votes
2answers
291 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 ...
3
votes
1answer
180 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 ...
2
votes
3answers
110 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 ...
3
votes
4answers
157 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 ...
2
votes
1answer
183 views

19 balls and a scale

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 ...
5
votes
1answer
127 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
0answers
67 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. ...
4
votes
2answers
501 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. ...
31
votes
4answers
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 ...
4
votes
4answers
224 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 ...
10
votes
1answer
351 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 ...
3
votes
1answer
141 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
3answers
234 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 ...
3
votes
3answers
209 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 ...
2
votes
3answers
360 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 ...
20
votes
1answer
866 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 ...
0
votes
2answers
299 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 ...
10
votes
9answers
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 ...
30
votes
7answers
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 ...
6
votes
1answer
264 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 ...
11
votes
3answers
576 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 ...
8
votes
2answers
347 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 ...
2
votes
0answers
38 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 ...
2
votes
3answers
2k 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 ...
10
votes
5answers
984 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 ...
8
votes
3answers
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 ...
6
votes
1answer
277 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 ...
5
votes
1answer
130 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 ...
4
votes
2answers
207 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 ...
6
votes
1answer
242 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
2answers
297 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 ...
13
votes
2answers
473 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 ...
15
votes
7answers
862 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 ...
9
votes
3answers
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,...
7
votes
2answers
321 views

“Balls in Boxes in a Sack” Weighing Problem

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 ...
4
votes
4answers
318 views

Weighing Counterfeit coins

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 ...
3
votes
1answer
166 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 ...
9
votes
4answers
627 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 ...
2
votes
1answer
79 views

Breaking Balance (Part B)

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 ...
7
votes
5answers
361 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 ...
6
votes
3answers
389 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 ...