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Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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9
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 ...
29
votes
7answers
3k 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
218 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
524 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
309 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
35 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 ...
0
votes
0answers
147 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 ...
9
votes
5answers
494 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 ...
7
votes
1answer
242 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
126 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
125 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
122 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
268 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
425 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 ...
14
votes
7answers
702 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,...
6
votes
2answers
268 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
274 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
150 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
465 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
65 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
342 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
345 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 ...
-2
votes
1answer
81 views

Reversed Weighings question [duplicate]

I hope this has an easy answer! A batch of $n$ coins has a single fake coin, which is lighter than the rest. The idea behind this puzzle is: What is the largest batch of coins that can have the ...
11
votes
5answers
645 views

Distinct ball weights but balance on the scale

You are given eight identical-looking balls and a two-sided scale. All of the ball weights are distinct, but if you put 4 specific ones on the one side, and the rest on the other side of the scale, ...
6
votes
2answers
343 views

$9$ coins into three groups

You are a lab assistant and your prof asked you something very specific: There are $9$ coins made of three different materials with different densities in front of you, but they look the same, divide ...
4
votes
1answer
455 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 ...
-2
votes
1answer
150 views

This weighs heavily on my mind [duplicate]

I have 9 coins that look identical, but one is heavier than the others. I want to identify that one. My brother has an old-fashioned balance scale that I can use, but I'll have to do annoying chores ...
3
votes
3answers
189 views

Optimal number of weightings in marble problem

Consider $N$ pieces of marble. The pieces of marble look identical to one another. One of the pieces is heavier than the other. In other words, out of the $N$ pieces, $N-1$ have the same weight and $1$...
4
votes
1answer
205 views

Find the fake bar in 2 weighing [duplicate]

You are given 8 equal sized bars of silver labeled a to h. You know for a fact one of them is fake, and the only measurable difference is weight. However you do not know if the fake bar is heavier or ...
5
votes
2answers
337 views

Weighing balls of three colors

You have six balls. Two are red, two are white, and two are blue. One ball of each color weighs 6kg. The other three all weigh 6.01 kg. How many uses of a two pan balance does it take to determine ...
1
vote
2answers
300 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 ...
2
votes
3answers
389 views

A balance with three pans

MATERIAL We have a set of 9 coins equally sized and shaped but with a different weight for each of them. We also have a very new three-pan balance which work in the following way: Three slots in which ...
1
vote
2answers
897 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 ...
4
votes
1answer
344 views

Fake and genuine coins

There are 14 coins, numerated from 1 to 14, and presented as an evidence at the court. The first 7 are fake coins, and others are genuine coins. Fake coins have all the same weight and they are ...
8
votes
2answers
406 views

Counterfeit Detector

You have a machine that lights up if counterfeit coin is placed in it. Any number of coins can be placed in the machine. It only lights up and does not indicate how many counterfeit coins are present (...
7
votes
2answers
559 views

Five balls weighing

Five identical looking balls have known distinct positive integer valued weights (let's say $w_1$, $w_2$, $w_3$, $w_4$ and $w_5$). You want to find weight of each ball using a digital scale with a ...
4
votes
2answers
255 views

Coin weighing puzzle

We have 5 boxes with 20 coins each. And coins of three boxes weigh 10, one of them weighs 9 and the other weighs 11. How can we differentiate between them by using a scale(digital, not the one with ...
3
votes
2answers
342 views

A Two-pan Non-Equal Arm Scale

There is a broken two-pan arm scale, consists of different weighed pans and different arm lengths. You are trying to weigh three different weights called X,Y,Z. You also know that the weights are ...
6
votes
2answers
768 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 ...
4
votes
3answers
362 views

Is it possible to measure 1 kilogram of sugar?

There is an iron kettle-bell which weighs 6 kilograms, an infinite amount of sugar, infinite amount of packets for it and a weighing scale which has two weighing pans. The scales are in equilibrium ...
14
votes
3answers
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 ...
12
votes
4answers
905 views

A different kind of weighing problem

A puzzle I enjoyed, from the November 1983 issue of the American Mathematical Monthly: Problem E3023: Proposed by J. G. Mauldon (a well-known retrograde analysis chess problem composer too!) You are ...
10
votes
1answer
204 views

Irrationality in the balance

Sensibilly -T ™ scales were out of stock, so Gramazon filled the order with a lousy Lopside® from Irreturnable Irrationals International, Inc.73205080...  How ...
6
votes
2answers
502 views

Determining integral weights

We have a balance scale, where can determine whether two quantities $a$ and $b$ satisfy $a>b$, $a=b$ or $a<b$. Given an integer $w_n$, we want to be able to distinguish between weights of $1,2,\...
4
votes
2answers
420 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.   &...
0
votes
1answer
2k views

The Heavy Pill Puzzle [duplicate]

You have 20 bottles of pills. 19 bottles have 1.0 gram pills, but one bottle has 1.1 gram pills. There is a weighing machine which calculates exact weight, and you have to find the heavy bottle by ...
8
votes
7answers
2k 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 ...
5
votes
2answers
410 views

Find the fake gold bracelet in the pile with only four weighings [duplicate]

Setup: A jeweler has a pile of eighty gold bracelets - all but one have the same weight. All the bracelets look the same including the one fake gold bracelet which weighs less than a true gold ...