Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

A strategy puzzle that is centered around scales, weights, and balances. Typically, in these problems one is given a set of identical-looking items (coins, stones, balls, tokens), and typically the goal is

  • to identify one item with a particular weight,

  • to divide the items into several groups with certain desired weights,

  • to verify whether the weights of the items satisfy a certain property.

with as few weighings as possible.

The underlying weighing mechanism might either be

  • a two-armed balance (with two pans): for comparing the weights of two sets of items with the possible outcomes "left pan is heavier", "left pan is lighter", "both pans have equal weight"

  • a calibrated one-armed balance (with a single pan): for learning the precise total weight of the item set in the pan

186 questions
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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 scale: If you press the TARE button, the scale's…
Snowball
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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 than 3.6 grams. We have a digital scale. How can…
student28
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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 weight positions per beam for a total…
humn
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Find a stone which is not the lightest one

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, instead you can only measure them by putting 10…
podloga123
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Six balls, six weighings

Six spheres, six weighings. If you grow impatient with the narrative, you can skip to the TL;DR, below. An engineer was walking across the street, on the way back from lunch, when bam, hit by a bus. She opened her eyes, to see a man standing before…
user3294068
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Find 2 heavy fakes among 11 coins on a 3-pan balance

I give you 11 coins, which look exactly the same. Among them are two fake coins. All genuine coins weigh the same. The fake coins are a little heavier than the genuine ones, and they may have a different weight from each other. You cannot…
Christian Semrau
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A balance with three pans, detecting the lightest pan (find the one lighter ball)

The following puzzle was told to me by a friend, Markus Götz, who put it online here: Deviating Ball Puzzles (pdf). After some searching, I did not find this puzzle anywhere else online. The only similar (but ultimately different) puzzle I found is…
Christian Semrau
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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 coins together, to get their total weight accurate…
Jaap Scherphuis
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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 level. In case of the same number of balls on…
TSLF
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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
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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, it is one gram like other normal coins. A certain…
TSLF
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Interesting Puzzle About Indian And Brazilian Marbles

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 weighs 11 units. Of the 8 boxes there is one box in…
Marieeee
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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 on the 5th floor.There is no available…
TSLF
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A balance with three pans, detecting the lightest pan (find the one heavier ball)

This is a continuation of the question A balance with three pans, detecting the lightest pan (find the one lighter ball). It was told to me by a friend, Markus Götz, who put it online here: Deviating Ball Puzzles (pdf). The three-pan balance Imagine…
Christian Semrau
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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. What are the number of test tubes which can be…
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