# Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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### A general solution to the decanting problem? (aka jug-pouring, water-pouring)

Take a look at these two questions: - A Set of Water Jug Challenges - Pouring problem Now I'm asking for a generalised solution to that problem. I define the problem as follows: You are required ...
3k views

### Determine the algorithm

So I was given this puzzle quite some time ago and just thought it would make a nice addition to this site: Your task is to determine the method how the result is determined from the given number. A ...
10k 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 ...
5k views

### N logicians wearing hats of N colors

N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
52k views

### A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
78k views

### Make numbers 1 - 30 using the digits 2, 0, 1, 8

It's 2018 so let's repeat last year's challenge with new digits. This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all four digits exactly once Allowed ...
5k views

### Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
24k views

### 100 Prisoners' Names in Boxes

Names in Boxes The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room;...
9k 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 ...
3k views

### The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
19k views

### Paying the Troll toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 ...
19k views

### Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
265k views

### 6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
5k views

### Pirates and gold coins

A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and ...
3k views

### Use 2 0 1 and 8 to make 67

Use $2$ $0$ $1$ and $8$ to make the number $67$ RULES You must use all 4 digits. Only the digits 2, 0, 1, and 8 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 82, ...
511 views

### Find the value of $\bigstar$: Puzzle 1 - Evaluation

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide to the following rules: Each symbol ...
20k views

### The Sheikh dies

The Sheikh dies, leaving behind three sons, 17 camels and the following order: His oldest son shall inherit one in two camels. His middle son shall inherit one in three camels. His youngest son shall ...
6k views

### The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
1k views

### Nerds, Jocks, and Lockers

Here's an oldie but goodie from The Daily WTF; I paraphrase to avoid copyright issues: A middle school math teacher, who also happened to be the P.E. coach, made the following deal with the non-...
302 views

### Find the value of $\bigstar$: Puzzle 2 - Switch-a-roo

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide to the following rules: Each symbol ...
264 views

### Find the value of $\bigstar$: Puzzle 3 - Substitution

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what number fits in the place of $\bigstar$. All symbols abide by the following rules: Each symbol ...
895 views

### Input/Output Problem #1

The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them. ...
2k views

### Make numbers 93 using the digits 2, 0, 1, 8

I have a 1 to 100 building challenge with 2, 0, 1, 8, all made but 93 is not made. I need your help! This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all ...
150k views

### 1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
5k views

### Hidden in plain sight - By what method do these images hide a prime number?

Note: This question has been severely edited from its original version to better fit the format of this site. Some answers below - including the accepted, correct answer - have been given based on the ...
11k views

3k views

### How do you solve the circular table problem?

One classic puzzle has many different forms, but the basic strategy is the same. Once upon a time there was a crazy king who had a very wise minister with him. The king had a habit of playing a ...
5k views

### No broken eggs puzzle

Three men went to buy eggs from an eggs seller: The first ordered half of the seller's stock plus half of an egg. The second ordered half of what's left in the stock plus half of an egg. The third ...
### Find the value of $\bigstar$: Puzzle 6 - Enclosed Operations
This puzzle replaces all numbers (and operations) with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. All symbols abide to the following rules:...