Questions tagged [weighing]
A puzzle that is centered around weighings and balances.
117 questions
10
votes
3answers
971 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
237 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
260 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
122 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 ...
6
votes
2answers
243 views
+100
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
55 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 ...
6
votes
5answers
320 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
225 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
80 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
600 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
336 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
224 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
131 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
185 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
196 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
318 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
225 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
360 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
637 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
323 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
394 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
428 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
241 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
283 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
585 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
355 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
873 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 ...
9
votes
1answer
198 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
448 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
355 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
406 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
159 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
183 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
307 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
votes
4answers
5k 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
71 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....
10
votes
6answers
7k views
1 Fake Coin among N Amount of coins
You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale.
You are asked to find the fake coin in totally 5 times weighing on the Pan ...
18
votes
8answers
2k views
30 fake coins out of 99 coins
You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
0
votes
2answers
284 views
Weigh eight balls and find the lighter one [duplicate]
There are similar puzzles but I think this one is different.
You are given eight metal balls. You know one weighs less than the rest.
You are given a balance scale. What is the smallest number of ...
7
votes
1answer
656 views
The different twins
The seesaw is filled with nine pairs of identical twins. All the kids weigh the same (e.g., they all weigh 100, but the actual numbers are irrelevant),
except for one set of twins. They are still ...
6
votes
7answers
709 views
A Two Faced Coin
A stack of 12 coins that looks identical are to be tested for the unusual one which become slightly lighter on one face and slightly heavier on the other face. If it is weighed standing on its side, ...
28
votes
13answers
3k views
15 Balls Sorting
This is a variant of 15 Balls Weighing.
You have 15 balls of 15 different weights, but the weights are so similar you can't tell them apart by feel. The balls are also identical by any other sense ...
11
votes
5answers
381 views
A Dozen Golden Eggs, Part 2
This is a variant of A Dozen Golden Eggs posted by TSLF, this time with the digital scale removed.
You have twelve golden eggs arranged on the shelf according to shell thickness, with weight tags in ...
