# Questions tagged [mathematics]

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

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### 1,1,1,-17,? What's the next number and what's the pattern

1,1,1,-17,? What is the pattern and what number comes next
1 vote
43 views

### Nothing complicated, just a simple principle

You're infront of a rather odd eight ball pool table with the holes covered up such that the whole table is perfectly flat. It has unusual inner dimensions, 9 and 26, with all balls (1-15) with radius ...
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### Factorials whose product is a perfect cube

Find two or more different positive integers the product of whose factorials is a perfect cube. How small can the largest of these be? How few can they be?
114 views

### What is this card matching game/trick?

As a kid I used to do this card game/trick a lot but I can’t remember what it is or how to do it anymore. All I remember is that it used math or counting. You had a certain amount of cards sort of ...
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### Iq question from mensa iq app [closed]

Anybody have an idea how to answer the attached question. Can't seem to figure it out!
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### Is this maths equation leading me through the first or second door?

I needed to speak to my professor who has gone into hiding. I followed her directions, leading me underneath the university until I got to corridor with two doors, labeled with the Roman Numerals: I ...
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1 vote
259 views

### Pipes and Tanks' Network

In the city XYZ, P is a water source from where water flows into the tanks – Q, R, S, T and U. The following diagram shows the network of the source and all the five tanks connected with pipes through ...
2k views

### Mensa IQ app: four boxes with four numbers each

Stuck trying to solve this question that popped up the other day. Spent the whole of the 15 minute test trying to find an answer to it.
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### If the door in Monty Hall is opened by a person without knowledge of where the prize is, and also does not reveal prize, do the odds change?

Here is the quiz variant. After the candidate chooses one door for the first time, and before the master (who knows which door hides the prize) intentionally opens another one to reveal no prize, an ...
58 views

### Find the last number in the pattern [closed]

There are 5 columns in a table. Column 1: Heart outline, Filled spade, Filled Clover Column 2: 2, 3, 12 Column 3: 3, 2, 18 Column 4: 4, 3, 24 Column 5: 3, 4, BLANK What goes in the blank and why? ...
1k views

### The universal ticket

I am submitting a very interesting problem from a French mathematical recreation site: http://www.diophante.fr/problemes-par-themes/g-probabilites/g2-combinatoire-denombrements/1434-g248-le-billet-...
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### Try to find the correct analogy according to given data [closed]

If: 12 = 616 and 11 = 252 and 9 = 8 then 15 = ? This question encloses a logic of association with a simple but trickily hidden explanation.
202 views

### The Pawn March Problem

The Pawn March Problem is something I just came up with, and I thought it was interesting enough to share. White has a line of $n$ pawns on an infinite chess board, all on rank 0 (negative positions ...
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### Taking turns adding a number 1,2,3 to a 3x3 matrix without repeating numbers in the rows or columns: does the first player always win?

Alice and Bob are playing a game on an initially empty 3x3 matrix. They take turns, and each turn: They add a number in {1,2,3} to an empty cell. They are not allowed to repeat a number in a row or ...
275 views

### Cover an n times n grid with non-diagonal non-intersecting n-1 shortest paths

This puzzle was given to me by PhD student colleagues. Suppose that you have a $n\times n$ grid. Is it possible, for a given $n$ to cover all its $n^2$ nodes with $n-1$ non-diagonal and non-...
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### Polyominoes inside a 10x10 grid

Can you place five dominoes, five trominoes, five tetrominoes, five pentominoes and five hexominoes inside a 10x10 grid, such that: No two polyominoes overlap No two polyominoes of the same size (by ...
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### The alien quantum-tunnelling hyperking labyrinth escape

Great title, right? Don't worry, I'll explain it. Here is the story. The inhabitants of planet Nuri have captured their arch-enemy, the hyperking of a neighboring planet (thus "alien"). ...
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### Multi-colored polyominoes inside a 7x7 grid

Can you place four red trominoes, four green tetrominoes and four blue pentominoes inside an 7x7 grid, such that: No two polyominoes overlap No two polyominoes of the same color touch each other ...
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### Shocking Singing Logic

$B = (\lnot C \land E) \land A$ $A = (\lnot E \lor D) \land *$ $D = \lnot A \land \lnot(B\lor E)$ $C = \lnot(E \lor B) \land (A \lor D)$ $E = (A \lor \lnot C) \land (* \land D)$ TRUE / FALSE What am ...
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### Tetromino in a Pentomino Lair

Inspired by this question: Can you fit twelve pentominoes (not necessarily distinct) and one tetromino inside a 10 x 10 grid such that they do not overlap or touch each other orthogonally (...
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### Flipping through the faces of a cube?

Let's place a cube on a table and flip it around a bit. In fact, flip it according to the following instructions: Flip forward twice. Flip left twice. Flip backward twice. Flip right twice. Assuming ...
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### Flipping Platonic solids

A cube is flipping on a table along its edges without sliding. If the cube flips two steps forward, two steps to the left, two steps backward, two steps to the right, then the cube is back to its ...
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### Fitting pentominoes inside a 10x10 grid

What is the most number of pentominoes that you can fit inside a 10x10 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically)? Bonus: what is the most number ...
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### Ten tetrominoes inside an 8x8 grid

Can you place ten tetrominoes inside an 8x8 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically) ?
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### Create all of the integers from 1 to 100 using 1, 5, 5, and 7

All four numbers must be used for each solution, but they may appear in any order. Permitted: the 4 basic mathematical operations, square root symbol (maximum twice per solution, and the 2 is implied)...
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### Sum Like It Simple

The three intersecting ellipses form seven curved regions. Place one tile from the seven candidates in each of these regions so that the tiles in any ellipse adhere to the corresponding rule. Show ...
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### Four pipes on a 8x8 grid

You are managing the construction of 4 water pipes on a 8x8 grid. The rules are the following: Each section of a pipe uses a whole grid cell. Pipes are composed of multiple sections connected ...
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### Reverse the bit order

There is a clever way to reverse the bit order of a byte, that I found here. In order to reverse bits of a number between 0 and 255 inclusive, perform the following steps: Multiply by 8623620610 ...
535 views

### Who is most likely to win all the chips?

Alice, Bob and Charlie each have 5 chips. Starting from Alice, they take turns to act in the order of Alice, Bob and Charlie. The $n$-th person to act must take a total of $n$ chips from their ...
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### The Game of Golden Squares

On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
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### Ages of Widow and Her Children

On New Year's Eve, a census taker gathering information calls a woman and asks specific questions about her family and their (integer) ages. She replies, "I don't like to give out specifics, but ...
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### What number should the first person announce?

Five people each announce a number in turn. The number must be an integer in the range from $1$ to $100$, and different from the ones already announced by others. The winner (or winners) of the game ...
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1 vote
114 views

### Letters and dashes... but without the numbers this time!

Previous Part Here's another fun puzzle! Decode this statement: ...
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### A Rotten Riddle

Someone gave me a scrap of paper and told me if I could solve this, I would get a prize. The only thing on the paper was the following: ...
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### Ernie and the Menacing Monopoles

While driving home from a fishing trip Ernie and I saw a road-side sign pointing down a gravel track that announced ‘MYSTERIOUS SOUTH SLOPING TREES’. It was getting well on into the afternoon, and I ...
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1 vote
65 views

### Numbers and Dashes again... but with letters this time!

Previous Part Here's a fun puzzle I created! Decode this statement: ...
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### Numbers and Dashes

Here's a fun puzzle I created! Decode this statement: ...
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### Entry to CIA Part #2

Previous Part: Part #1 After successfully completing Part #1's puzzle, you receive another message from the CIA on your black screen: Dear Reader, we are glad to state that you have been accepted ...
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### Entry to CIA Part #1

As I searched for different topics on Google, my whole screen suddenly went black and gave me this letter: Dear Reader, if you have come across this message, you may be applicable for the CIA. We are ...
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2k views

### Twenty-four trees in eighteen rows of four

A very old puzzle, #146 from American Agriculturist, April 1865: How may twenty-four trees be planted in exactly eighteen rows, with four trees in each row? A row consists of a number of trees in a ...
254 views

### Good Rectangles and Evil Numbers - Integrated

Good Rectangles and Evil Numbers - Integrated Original: Good Rectangles and Evil Numbers Good Rectangle We define a good rectangle with base $x$ as a rectangle in which $\frac lw = x$ where $l$ ...
677 views

### What is 12 in this same pattern?

7 = 31674ZS 8 = 883011SO 9 = 166037352UR 10 = 434782608W...
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### Compact mathematical expression [closed]

Make a mathematical expression whose value is equal to 2 that uses all the digits 0, 1, 2, ... 9 exactly once and uses as few other mathematical symbols as possible.
444 views

### Seven robot ants that stay forever on a rod

You must place 7 robot ants on a long rod and set each of them to move left or right starting at time 0. You can set any positive speed for each ant. When 2 or more ants meet, they turn around. When ...
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1 vote
141 views

### Honeycomb puzzle with hexagons [closed]

Can you place the numbers 1 through 9 in the honeycomb so that the sum of the numbers in the adjacent hexagons is a multiple of the number in the hexagons? This must be true in all hexagons. The top ...
919 views

### A peculiar number

A five digit number is multiplied by 9, the resulting number is reverse of the given number. What is the five digit number? This question was asked in KVPY 2020, SA.
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### Robot ants that stay forever on a rod

You can place any positive number of robot ants on a long rod and set each of them to move left or right starting at time $0$. You can set any positive speed for each ant. When 2 or more ants meet, ...
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218 views

### I’m right 4 times

I can be a 2, or a 4. Split me in half and I can become a 6, but do it wrongly and I’ll be an 8. Lengthen my sides and I am not myself. anymore.
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### Pick cards from a table

2022 cards are arranged on the table in front of us. Each card shows a number that we can see. For each of the numbers from 1 to 2022 inclusive, there is exactly one card that depicts it. We have the ...
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