# 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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### Nine touching clocks [duplicate]

There are nine 12-hour clocks arranged in a 3x3 grid, as shown in the diagram. The long minute handles of the left two clocks are touching, while the others are not. Two minute handles touch if they ...
1answer
1k views

### Four touching clocks

There are four 12-hour clocks arranged in a 2x2 grid, as shown in the diagram. The long minute handles of the left two clocks are touching, while the others are not. Two minute handles touch if they ...
1answer
262 views

### Multiplying English numbers is strange too

It seems that the English-speaking people multiply the numbers in the very same way that the Portuguese add them: while the latter say that 2+2=8, the former claim that 2×2 is 8: ...
1answer
524 views

### What was my friend talking about?

Can you help me understand what my friend was saying to me the other day? He's really smart (a math savant AND a huge fan of those cryptic crossword things), so I'm trying to spend time with him and ...
1answer
85 views

### A 4x3 grid puzzle with one missing number [closed]

I've been trying to solve this but I still can't find the solution, could someone help me please? Transcription: 11 6 8 17 12 ? 25 34 19 19 28 11 and choices are A. 13 B. 15 C. 16 D. 19
1answer
180 views

### Unusual sequence of fractions

Let's have the following sequence of fractions: $\frac{156}{51}, \frac{756}{251}, \frac{3756}{1251}, ?$ . What fraction replaces the question mark?
3answers
397 views

### A circle touches two sides of a triangle and two of its medians

A circle touches two sides of a triangle and two of its medians. Prove that the triangle is isosceles. This problem came from the Mathematical Digest issue 62 (Jan 1986) which in turn cited a Russian ...
2answers
155 views

### How many L-shaped pieces will not be used to make cubes?

The puzzle is as follows: The figure from below belongs to a didactical toy which is comprised of 32 congruent wood pieces as indicated in the figure. Each piece is made up by three cubes whose edges ...
1answer
136 views

### What is the perimeter of a pentomino which can tile this heart-shaped board?

The puzzle is as follows: The figure from below shows a board that is made up of 30 squares whose sides are of 2 centimeters each. Such board must be split in six congruent pieces. These must be made ...
1answer
101 views

### Filling a 26x36 grid with trominoes

Let's have 312 L-trominoes of three different colors, 104 trominoes of each color. Can you fill a 26x36 grid with these trominoes without two of the same colors touching side-to-side anywhere? In ...
1answer
119 views

### Join neckles to make one [closed]

Join five three-link chains to one 15-link chain To join two chains, you must cut, and then re-weld, a link. The new chain should have exactly two ends (no more, no less). The questions is what is ...
1answer
90 views

### How many figures to cover the kitchen floor?

The puzzle is as follows: Figure 1.1 shows a kitchen floor that is made up of 30 squares whose sides measure 1 cm in length and in Figure 1.2 a tile that is made up of 5 squares whose sides also ...
2answers
662 views

### Balancing the marble game (Red marbles are OP, please nerf)

Ash and Bree are playing a simple game of chance: They fill a bag with small marbles coloured red or blue. They take turns to draw a marble from the bag without looking, then: If Ash draws a red ...
1answer
256 views

### Arrange candies without repeating pattern

The following puzzle had been posted before but I couldn't understand the only answer that was given there, which was by @neodne . So, I created this post asking someone to explain neodne's answer to ...
1answer
116 views

### A math sequence, but also a English sequence!

What are the numbers in the question marks? 0, 1, 2, ?, 5, 6, 8, ?, 40, 46, 60, ?, 84
1answer
113 views

### Probability of a successful DT Cannon

In multiplayer Tetris, there are a number of opening setups that let you send powerful attacks very quickly. One popular opening is the DT Cannon, which allows the player to very quickly send a T-Spin ...
1answer
126 views

### Four-Number Door Puzzle

So I had an idea for a number-based door puzzle for a TTRPG campaign that could readjust itself every time a wrong guess is made. Here's the basic premise: Given two numbers, find two more numbers in ...
2answers
197 views

### Pirates dividing booty around a circular table

A group of pirates have plundered one of his majesty's cargo ships and they all carried as much gold coins as each one could find. When they get back to their ship, they sit at a round table and pass ...
1answer
147 views

### Swapping eggs puzzle

You can try this with pencil and paper, or make it a physical puzzle you can try out with your kids if you have one of those large 3x6 egg cartons laying around. Imagine you have 3 rows of 6 spots. ...
1answer
150 views

### Non-increasing arrangement

We are arranging the numbers from 1 to 8 in an order so that three consecutive terms cannot be increasing. For example, 12345678 isn’t allowed but 81436572 is. How many ways are there to do it? Please ...
1answer
77 views

### Factorizing complex numbers [closed]

Let's have the following number $(3i-\frac{5}{3})^3$. What is the trick to factorizing this number in more than one way?
1answer
128 views

### Fill in a 6x6 magic multiplicative magic square

Let's say you fill in a 6 by 6 square with the numbers 1, 2, ..., 36. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
1answer
115 views

### A Clear, Simple, Geometry Problem [closed]

Draw a shape consisting of all the points equidistant from a specific point. Furthermore, draw a segment passing through a side of the shape exactly twice, and draw another segment so that it also ...
1answer
438 views

### Fill in a 4x4 multiplicative magic square

Suppose we have 4 by 4 grid with numbers 1, 2, .., 16. Can we fill the grid so that the product of the first row is equal to the product of the first column, the product of the second row is equal to ...
2answers
257 views

### Least cuts to get 44 rods from a metal grid

The puzzle is as follows: Suppose that you have a metal structure made by brass wire. Assuming that you must get 44 rods of the same size each. What is the least cuts to be made using an electric ...
1answer
122 views

### Minimum cuts to make a rectangle into a square, allowing bending

The puzzle is as follows: Mike has a thin sheet of cardboard which is 96 centimeters large by 24 centimeters wide and a guillotine whose maximum cut length is 80 cm. Assuming this guillotine can cut ...
0answers
275 views

### Fill in a 5x5 multiplicative magic square

Let's say you fill in a 5 by 5 square with the numbers 1, 2, ..., 25. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
1answer
98 views

### Vowels, consonants and Mathematical Shapes

Your aim is first to select at least three different mathematical shapes. For instance, you could select "a losange", "a disk" and "two lines". You must then ensure that ...
1answer
167 views

### Universal bisectors

A bisector is something that cuts some other thing into two equal pieces. More concretely, assume we are given a reasonably well-behaved (for example, compact) 3D object and we are looking for planes ...
0answers
86 views

### Bisecting a 3D object into two equal volume objects - 2

Given the following 3D object and means of an unmarked ruler to draw lines on its surface define a straight cut that will split it into two objects with the same volume. Hint: It seems to have at ...
2answers
203 views

### Primes and squares in a grid

i) Place thirteen different three-digit prime numbers in the empty cells of this grid. ii) Now place thirteen different three-digit square numbers in the empty cells of this grid. How many solutions ...
1answer
91 views

### Relations between numbers taken three at a time [closed]

Let's have the following numbers. $(5i+\frac{1}{2})$, $(2i+3)$, $(\frac{-101}{8})$, $(7i+4)$, $(5i+1)$, $\frac{(40i-97)}{8}$. How are these numbers related when taken three at a time? Operations ...
1answer
1k views

### Find three ways of forming the number 100 using 3,3,5,7

As it says in the title. Rules: anything not explicitly allowed is forbidden. use 3, 3, 5, 7 and multiplication, division, sum, difference, unary minus, and exponentiation in any order. Parentheses ...
1answer
205 views

### Three white queens, two white knights, and one rook on a chess board

On an 8 x 8 chessboard, place three white queens, two white knights, and one white rook so that every cell of the board is under attack by at least one piece not standing on it. Source: https://www....
1answer
81 views

### Number of turns for two wheels to bring edge-points together

The puzzle is as follows: We present you below this riddle. A certain mechanism opens a gate of a maximum security lab. It just happens that a glass lets you see the mechanism and you know the ...
0answers
68 views

### Fair and square island hopping [duplicate]

If amateur fiction is not your thing skip to the bottom. As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh ...
3answers
594 views

### Calculation - the hard way

This is a puzzle I love to play with my math students and I hope you will enjoy it too: You are given the numbers 1, 2, 3, 4, and 5 exactly once. Your target is a number, e.g. 36. Can you create a ...
1answer
229 views

### How to get the least possible sum in a closed loop set of squares?

The puzzle is as follows: The figure from below represents a set of 12 squares joined forming a closed loop. By using only the numbers from 1 to 12 fill in the blanks. The condition is that, without ...
2answers
150 views

### How many lines are needed to connect all smiling toasters in a 4x4 grid?

The puzzle is as follows: How many straight lines do you need to draw the least possible to join all the smiling toasters if you should not raise the pen or go over any line already drawn? Remember ...
1answer
336 views

### Two knight tours on a 4x4 grid

Two knights are placed on opposite corners of a 4x4 grid. Can you move* each knight 7 times, such that each cell of the grid is visited exactly once by exactly one of the knights? *Note that a knight ...
2answers
228 views

### Minimize the longest King chain on a 6x6 ternary grid

This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board Given a grid filled with numbers, we define a King chain to be a path on the grid such that: The path ...
1answer
125 views

### Minimize the longest King chain on a 7x7 binary grid

This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board Given a grid filled with numbers, we define a King chain to be a path on the grid such that: The path ...
0answers
192 views

### Choosing squares on a square board [closed]

I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
1answer
2k views

### A Math Riddle: But the math does not add up

Grandpa had a lot of different books of stamps on his desk. He was counting them. I was curious. “What are all those stamps Grandpa?” “I just got back from the Post Office son and bought a bunch of ...
2answers
243 views

### All possible locations of a robot going from $(x,y)$ to $(x+y, y)$ or $(x,x+y)$ [closed]

Suppose I had a little robot on the coordinate grid that moves according to the following rule. If it's at the point $(x,y)$, it can move to either $(x+y,y)$ or $(x,x+y)$. If the robot starts at the ...
1answer
133 views

### Solving the equation $A^4=B^4+C^4$ [closed]

Let's have the following numbers: $2\sqrt7$, $\sqrt{\frac{7\sqrt{674}-168}{2}}$, $3\sqrt7$, $-\sqrt{\frac{7\sqrt{674}-168}{2}}$, $2\sqrt7$ Can you put these numbers into three different groups A,B,C ...
2answers
91 views

### Dividing the first 10 numbers into two groups with similar product

Can you paint all numbers from 2 to 10 with red and blue colour, such that the product of all red numbers is as close as possible to the product of all blue numbers?
2answers
111 views

### How many have to enter the building so their birthday matches?

The riddle is as follows: Looking at his watch a doorman from an hotel in New York notices that 280 people are inside. Suddenly he begins to ponder the following. How many people should have to come ...
1answer
139 views

### Seven letters riddle

Hoping it is a never-seen riddle, here is the problem. We have seven letters A,B,C,D,E,F,G. Each letter is associated with a unique number between 1 and 10. We know the following: D is 3 units ...
7answers
838 views

### Minimize the longest King chain on a 5x5 binary board

Given a grid filled with numbers, let's define a King chain to be a path on the grid such that the path can be traversed with chess King's moves (moving to one of 8 adjacent cells at a time), the ...