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A puzzle that is centered around weighings and balances.

-2
votes
1answer
111 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
167 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
155 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
302 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
130 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
330 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
388 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 ...
3
votes
1answer
289 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
384 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
347 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
200 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
234 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
292 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
323 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
824 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 ...
8
votes
1answer
188 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 ...
5
votes
2answers
380 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
251 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
440 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
396 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
471 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
127 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
173 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
297 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
2k 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
154 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
68 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
4k 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 ...
10
votes
3answers
831 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
193 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
645 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
694 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
368 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 ...
16
votes
1answer
697 views

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 ...
4
votes
2answers
135 views

Selecting weights to minimize weighings

In this weighing problem objects of four different weighs are to be identified with four weighings with a balance scale. Now given that the four weights are all different, on one hand, there are $4!=...
25
votes
2answers
2k views

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 ...
-4
votes
2answers
230 views

Shortest number of attempts to solve this issue [duplicate]

There are 9 identical balls but only one of them has a higher weight. You are also given a weight balance. How many attempts would you require to identify the ball with the extra weight and how?
12
votes
2answers
795 views

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 ...
13
votes
6answers
2k views

15 balls weighing

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, ...
8
votes
2answers
692 views

Lots of Gold Golden Coins and a Scale

Following my previous question: Lots of Gold Stacks and a Balance Scale You are given 10 stacks, each stack consisting of N golden 10g-coins and a digital scale with perfect precision that shows ...
7
votes
3answers
801 views

Forty-six genuine and two fake coins

Inspired by this puzzle. In the country Dragonia, 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. It is ...
9
votes
6answers
702 views

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 ...
9
votes
3answers
529 views

The King's New Accountant

The king of Ebonchester has just returned from his recent conquests of Baronshire and with him he brought four cart loads of plunder. However Baronshire is known for its lacklustre fiscal regulation, ...
6
votes
1answer
311 views

Minimum number of tries to find the balance!

There are 8 distinct weights and a two-pan equal arm balance scale, and you know the weights' weight order: the lightest is numbered as 1 and the heaviest is numbered as 8 and the rest accordingly. ...
2
votes
1answer
423 views

Another 2016 coins and a balance

This continues the puzzle "2016 coins and a balance". Again, there is a balance with two pans on the table. Again, the display on the balance tells the difference between the weight in the left ban ...