Questions tagged [weighing]

A puzzle that is centered around weighings and balances.

181 questions
Filter by
Sorted by
Tagged with
2k views

A balance with three pans, detecting the lightest pan (find the two heavier balls)

This is a continuation of the question A balance with three pans, detecting the lightest pan (find the one heavier ball). It was told to me by a friend, Markus Götz, who put it online here: Deviating ...
371 views

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 ...
540 views

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 ...
1k views

Different Ball Puzzle

You are working in a ball factory, where balls of weight 1U, 2U, 3U ... 8U are made in 8 sections. One day, you are given 1023 black balls , all (except one special ball) from section 1, meaning ...
• 5,114
4k views

121 coins and a balance

Inspired by this puzzle... You have $121$ apparently identical gold coins. At most one of these is fake, and weighs a different amount than a genuine coin. In front of you is balance with two pans. ...
• 32.1k
4k views

Four coins (plus one) and a balance

Someone gives you 4 apparently identical golden coins. You know that among them there could be exactly one fake coin, and that a fake coin hasn't the same weight of a golden one. In your pocket you ...
• 2,830
193k views

Brooklyn Nine-Nine Riddle: Weighing Islanders [duplicate]

A brain teaser posed by the character Captain Ray Holt of 'Brooklyn Nine-Nine' played by Andre Braugher during episode 18 of season 2: "There are twelve(12) men on an island, eleven(11) weigh ...
3k views

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 ...
• 12.8k
159 views

Catch the fraud! [duplicate]

There are 10 gold smiths in the town and a rich businessman wants to collect 1kg of pure gold. So he informs each person to bring 10 balls of pure gold, each weighing exactly 10g. So altogether he ...
846 views

Spot the tumbler

There are 4 identical tumblers each filled with the same number of 1 kg balls. One of these four tumblers contains all defective underweight balls. You have a weighing scale which you can use to weigh ...
• 69
452 views

Twenty weights and a balance

On the table there are twenty weights with masses $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $11$, $12$, $13$, $14$, $15$, $16$, $17$, $18$, $19$ and $90$ grams, and a two-armed balance with ...
• 45.4k
1.4m views

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 ...
• 341
1k views

A golden weight of 11111 gram

Cosmo puts a golden weight of 11111 gram into the right pan of a balance. Then Fredo starts adding his bronze weights to the balance: first Fredo adds a bronze weight of 1 gram to one of the pans; ...
• 45.4k
1k views

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 ...
• 45.4k
2k views

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 ...
• 45.4k
3k views

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 ...
• 5,718
583 views

Balancing all but one weight

You have an odd number of tokens whose weights are known whole numbers, and they don't all have the same weight. Show that there's a token you can remove so that the remaining tokens can't be split ...
• 26.3k
4k views

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 ...
• 7,050
10k views

A King and his Servants [duplicate]

A king sent 10 of his servants out to buy him each 10 gold rings. Each ring should weigh 10 grams, and altogether there should be 100 gold rings. One of the King's spies told him that one servant had ...
4k views

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 ...
• 209
594 views

You are an intrepid explorer who has been caught in a trap by a primitive tribe. They lock you in a room with no exit but one door. The door has a pressure sensitive release - incorrect pressure ($>... • 12.8k 4 votes 1 answer 710 views Which one is the lightest marble? There are 8 marbles that one of them is lighter than the others, and all other seven marbles have the same weight. There is a balance scale that you can use it twice or once. Is there any way to find ... • 5,718 -2 votes 1 answer 827 views Find the Different Sugar Cubes [duplicate] There are 10 Boxes, each contains 1000 sugar cubes. The sugar cubes in 9 of the boxes are 10 grams each and the other box has 9 gram cubes. There is a digital scale that you can use it ONCE. (i.e. ... • 5,718 23 votes 2 answers 12k views 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 ... • 2,436 9 votes 2 answers 787 views Middle weight puzzle There are 100 white and 101 black balls. All the balls have different weights. Balls of the same colour look the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is ... • 16.1k 3 votes 1 answer 578 views $N_{max}\$ balls in 3 weightings

This is a small generalization of well known 12 balls puzzle: You are given two-sided scale and some number of balls. All balls have the same weight but one. It is of a different weight, although ...
• 16.1k
4k views

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 ...
1 vote
2k views

Minimum number of weights you need to define any integer weight from 1 to N

Following this question What's the fewest weights you need to balance any weight from 1 to 40 pounds? I am interested what is the minimum number M of weights you need to define any integer weight ...
• 16.1k
13k views

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 ...