Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

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-2
votes
0answers
55 views

Find 1 fake coin out of 10 coins (1 fake + 9 Original) in minimum comparisons [duplicate]

I have 10 coins where 9 are Original and 1 is Fake, which means the Fake one coin is either Heavier or lighter then Original coin. so in how many minimum comparison we need to find fake coin. links ...
5
votes
1answer
122 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
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2answers
103 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
111 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
251 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
416 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
648 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 ...
10
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
256 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
272 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
143 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
426 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
60 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
330 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
233 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
635 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
338 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
439 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
142 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
186 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
203 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
328 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
246 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
369 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
782 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
335 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
396 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
481 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
249 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
304 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
701 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
358 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 ...
13
votes
3answers
3k 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
887 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
199 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
484 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
386 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 ...
9
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
408 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 ...
1
vote
1answer
482 views

Find the minimum number of steps that we can arrange coins according to their weight

We have $20$ coins, every step we can give $10$ coins to a person and he will tell us the order of their weights. Find the minimum number of steps that we can arrange coins according to their weight. ...
0
votes
1answer
166 views

What weight of Weighing scale bars shop keeper should buy? [duplicate]

Story: Years ago there was a poor shop keeper who had a small amount of money enough to buy only FOUR weight bars for his an old weigh scale. Now the problem is he can buy only FOUR weight bars and ...
0
votes
4answers
186 views

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 ...
6
votes
1answer
309 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 ...
0
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4answers
6k 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:
6
votes
6answers
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 ...
6
votes
1answer
157 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
10
votes
9answers
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 ...
0
votes
0answers
74 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....