Questions tagged [weighing]
A puzzle that is centered around weighings and balances.
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Need Thorough Explanation of Coin Weighing Puzzle Solution
One of the coolest things I've seen on Puzzling is this puzzle, and especially the solution in 7 static weighings posted by Julian Rosen.
I have revisited that solution many times over the years, ...
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Balance Puzzle Find at most 2 counterfeit coins out of anywhere from >=3 # of coins
2 fake coins from a pile of 30 coins
The real coins all weigh the same, and the fake coins weigh the same. The fake coins weigh less than the real coins.
The difference in the one I am trying to solve ...
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Finding the weights of 3 coins
I have 9 coins; 3 coins each of 3 denominations.
Coins of the same denomination all weigh the same.
Each coin weighs an exact whole number of grams, and at most 9 grams.
I can weigh any subset of my ...
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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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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?
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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 ...
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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 ...
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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. How many objects of different weights can you weigh at ...
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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 ...
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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 ...
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⌈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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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19 balls and a scale [duplicate]
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 ...
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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 ...
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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. ...
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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.
...
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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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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 ...
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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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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 ...
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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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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 ...
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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 ...
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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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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 ...
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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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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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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 ...
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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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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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Gold, silver and bronze in the balance
Equivalent to finding three heaviest coins in order of weight,
on a balance that holds one coin on each side.
(Simplified, with some Wikipedia references corrected, from the original puzzle.
The ...
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"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 ...
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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 ...
user57107