Questions tagged [weighing]
A puzzle that is centered around weighings and balances.
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Twelve balls and a scale
You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...
user88
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Thirty genuine and seventy fake coins
In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions:
All genuine coins have the same ...
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Coin weighing with a single weighing device
You have 12 coins which each weigh either 20 grams or 10 grams. Each is labelled from 1 to 12 so you can tell the coins apart. You have one weighing device as well. At each turn you can put as many ...
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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 ...
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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 ...
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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 ...
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Unknown weight of four identical objects
Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you ...
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What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale by placing a certain combination of these weights onto ...
user88
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Coin weighing problem
You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision.
You know that all stacks of coins are made from gold, weighing 10 grams per ...
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Brooklyn 99 riddle: Weighing Islanders [duplicate]
This one comes from this week's Brooklyn Nine-Nine episode!
There is an island with 12 islanders. All of the islanders individually weigh exactly the same amount, except for one, who either weighs ...
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answer
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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 ...
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Trapped in my Cellar
I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
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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 ...
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A Dozen Golden Eggs
Twelve golden eggs are arranged on the shelf according to shell thickness with weight tags in ounces. You've been told that two of the eggs were swapped by some culprit!
You must put them back again ...
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Two genuine and two fake coins
In the country Argonia, there are only two types of coins: genuine ones and fake ones.
All genuine coins have the same weight, and all fake coins have the same weight.
The weight of a genuine coin is ...
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Fifty-two genuine and two fake coins
In the country Borgonia, there are only two types of coins: genuine ones and fake ones.
All genuine coins have the same weight, and all fake coins have the same weight.
The weight of a genuine coin is ...
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Weighing in 2015 different ways
This question was inspired by something I realized while thinking about @Gamow's Weighing in 89 different ways.
You have a two-pan balance and $2015$ weights, with masses $1,2,4,\ldots, 2^{2014}$. ...
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Evaporating coins
In the country of Dalgonia, there is only one type of fake coins and only one type of genuine coins.
All genuine coins have the same weight.
All fake coins have the same weight.
Fake coins and ...
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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 ...
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Why are all numbers from 1 to 2N covered by weights with powers of 3?
This is from What's the fewest weights you need to balance any weight from 1 to 40 pounds?
Suppose you want to create a set of weights so that any object with an integer weight from 1 to N pounds ...
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15 Distinct Weights' Sorting
There are $15$ balls. Each of them has a different weight.
You want to sort them according to their weights.
You have a friend who will help you with his scale to do this.
At each weighing process, ...
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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 ...
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Twelve balls on a scale, where one ball is lighter and another is heavier
Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
user88
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Radioactive Rods
You have 8 identical looking rods, 2 of which are radioactive, though you don't know which. You also have a box which can test for radioactivity, which can hold any number of rods. After the test, the ...
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Lots of Gold Stacks and a Balance Scale
You are given X amount of stacks of golden coins, each stack consisting of ten (10) golden coins and a digital balance scale with perfect precision that shows how much difference between weights you ...
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Using a balance scale the minimum number of times, find the median weight person
There are 15 person with different weights.
What is the least number of tries required to find the middle (median) weight person? How?
The only tools you have is your brain and a balance scale with ...
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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 ...
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Twenty-four coins
I have twenty-four identical-looking coins, but two are fake and weigh possibly different from each other, though definitely different from the remaining genuine coins. I have a weighing scale and a ...
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Determine your weight from 2 different answers from 2 weighting scales
You have 2 movable weighing scales.
Their least count is 1 gram.
You have tried both to find out your weight, but they give you different answers.
You do not know whether both of them are ...
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N balls and a scale
The question of twelve balls and a scale is probably the best-known example of the "find the ball of a different weight" problem. But does it generalize? Is there a general way to find a weighing ...
user88
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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 ...
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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 ...
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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 ...
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4
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Rank the Fencers
There are five fencers. Each has a particular skill level, all of which are different. When two fencers duel, the one with the higher skill level always wins.
How many duels do the fencers need to ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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Using a balance to determine any weight with a set of weights weighing powers of 3
There is a scale with an object on the left-hand side, whose mass is given in some number of units. Predictably, the task is to balance the two sides. But there is a catch: You only have this peculiar ...
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212 weights of 1 gram
Fredo owns a balance with two pans and 212 weights, each of 1 gram.
Fredo proudly announces to Cosmo that his weight system has the following stunning property:
For every integer weight $W$ with $1\...
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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 ...
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Weighing in 89 different ways
On the table, there is a balance with two pans together with ten weights
ofrespectively 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512 grams.
Cosmo takes a coin out of his pocket, shows it to Fredo and ...
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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....
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Fewest possible weighings to determine which ball is heavier/lighter
You are given 4 balls, all equal in weight except for one that is either heavier or lighter. You are also given a two-pan balance to use. In each use of the balance you may put any number of the 4 ...
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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 ...
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10
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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 ...
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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 ...
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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 ...
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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,...
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