# 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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### What function is it?

A function of one variable $y = f(x)$. However, I suspect that the function does not need to necessarily be strictly mathematical. If $x = 1$, then $y = 0$. If $x = 2$, then $y = 0$. If $x = 10$, then ...
2answers
74 views

### Show that no lines need cross [closed]

There are n red points and n blue points in the plane. Show that you can always join all the red and blue points with straight lines so that no two lines cross. Each point can have exactly one line ...
2answers
337 views

### Pentomino tiling on wrap-around 5x5 grids

It is known that P pentominoes cannot tile a 5x5 square board. Q1: If the east and west edges of the 5x5 square board are "wrapping around" (if you move a piece through one of the edges, the ...
1answer
131 views

### Guess game of Dwarfs [closed]

Kate and N dwarfs are playing a dwarf guessing game. In the beginning there are five empty boxes numbered with the numbers 1, 2, 3, 4 and 5. According to the rules of the game, Kate places at least 1 ...
5answers
169 views

### A Triad of Pies

Make the 41 integers between -20 and 20 (-20, -19, ..., 0, 1, ...20) using only the four basic arithmetical operations, square root, the floor function, and, Surprise Surprise, exactly 3 π’s. No more ...
4answers
641 views

### Make numbers from 1-10 with 5 3s

In this puzzle book, I came across a question that goes like this: Make the numbers from 1-10 using 5 3s. Rules: You are only allowed to use the four basic arithmetic operators ($+, -, \times, \div$...
1answer
223 views

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

Given the following object - box of which a rectangular pyramid is removed. By means of unmarked ruler, draw lines on the surface of the object to guide cuts of the object into two objects with the ...
1answer
230 views

### Primes Number Sequence

Find the pattern in the sequence: 10 11 21 247 29 391 ? ? ?
0answers
111 views

### Helping a team guess a correct number without prior knowledge [duplicate]

I am new here and would like to request your explanation for a riddle I saw. It is quite interesting but I don't understand it and would like your assistance to understand what's going on, how to &...
1answer
161 views

### Assemble lozenges

You have a large number of 60° rhombi called "lozenges." Each lozenge has its edges marked with four distinct symbols drawn from an infinite alphabet. Lozenges may be rotated by 180° or ...
1answer
123 views

### Domino diamonds

You have a large collection of dominos, each labeled with two distinct symbols drawn from some infinite alphabet. The symbols have 180-degree rotational symmetry so dominoes can be rotated. In other ...
1answer
143 views

### Variation of 100 prisoners [duplicate]

There are 100 prisoners, each prisoner is given a number between 1 and 100 without knowing which number, the number can repeat and not all of the numbers must be given. Each prisoner in his turn can ...
3answers
202 views

### A political party survey and the number of people in it

There are 6 major political parties in a country. An organization conducted a survey for these 6 major political parties to see what people are going to vote for. The results of the survey, in ...
9answers
3k views

### “We accept 20% of candidates and I'm 90% good at my job…” [closed]

There is a famous investment firm where a partner was known for having candidates walk into the room without a greeting, sit across from him at a huge desk, and start right away by asking: "We ...
1answer
237 views

### How many shapes can you form with squares? [closed]

There is a 6 by 6 dot-grid. You will draw two squares by joining the dots. The squares cannot have common dots/points or areas. Rotations or reflections of a drawing are considered distinct. In How ...
1answer
122 views

### IQ Test question - numbers inside a grid - math

There must be a better way of solving. Can someone tell me what is the correct answer and reasoning? Thank you. Transcription of the image: 3 4 5 5 6 16 8 12 52 14 14 ?
2answers
456 views

### When do decimal-coded binary numbers XOR to zero?

Background definition: XOR on numbers Given two non-negative integers $x$ and $y$, let $x\oplus y$ denote the bitwise exclusive or (XOR) of the numbers $x$ and $y$. This is the result of writing $x$ ...
1answer
433 views

### IQ Test question - numbers inside a 4x3 grid

I could not solve a question from an online IQ test: Transcription of image: What is the number in the * cell? 9 38 47 4 6 35 42 * 12 21 23 27 The options were: 10, -5, 32 and 18 The only pattern ...
4answers
444 views

### Crossing out every second number

Write down all integers from 1 to 1000. Cross out the first number and every second number after that. So you will cross out 1, 3, 5 and so on. Now repeat the process exactly - cross out the first ...
3answers
371 views

### A theorem about angles in the form of arctan(1/n)

There is a famous classical geometry puzzle about the angles formed by integer coordinates: What is the sum of angle A and B in the following image? Do not use any advanced mathematics such as ...
1answer
99 views

### Construct a Triangle with Triangles

If you have a very large but finite number of equilateral triangles (of any/all sizes) is it then possible to construct an isosceles triangle? By isosceles I mean a non-equilateral isosceles triangle. ...
3answers
700 views

### Reconstructing World Cup results

In the group stage of the World Cup, teams compete within eight groups of four teams each. Each group plays a round-robin tournament, in which each team plays three matches, one against each other ...
2answers
229 views

### Anne and Bernard's marbles

Anne and Bernard have between them 100 marbles, Anne the most. Some in each bag of their marbles are red, the rest, though fewer, are blue. If Anne draws at random two marbles from her bag of marbles, ...
1answer
156 views

### Unexpected number relations

Let's have the following numbers: $\sqrt{\frac{2069}{24}}$, $11$, $\frac{1397}{24}$, $\sqrt{\frac{2069}{24}}$, $3$, $\frac{2741}{24}$,$13$, $\sqrt{\frac{2069}{24}}$, $91$. Transcription: square root ...
1answer
320 views

### Math sequence. What number comes next?

I have created a pattern that is fairly interesting. It is discoverable from a geometric shape. The sequence begins: 1,2,4,9,1,18,1,2.... It is a repeating pattern. It could be an infinite repeating ...
1answer
206 views

### n rows and 18 columns

I haven't posted for a long long time, so here is an interesting combinatorics problem! There is a table with 𝑛 rows and 18 columns. Each of its cells contains a 0 or a 1. The table satisfies the ...
2answers
254 views

### Four brothers of different heights - confused over the answer [closed]

The puzzle is this: Next door to me live four brothers of different heights. Their average height is 74 inches, and the difference in height among the first three men is two inches. The difference ...
4answers
782 views

### Neighboring sums 5x5 game

You start with an empty 5x5 grid. At each turn you choose an empty cell and place a value in it. The placed value is given by the following rules: If the chosen cell has no neighboring (horizontal or ...
4answers
940 views

### Neighboring sums 4x4 game

Here is an interesting game. You start with an empty 4x4 grid. At each turn you can choose an empty cell and place a value in it. The placed value is given by the following rules: If the chosen cell ...
1answer
307 views

### Forming pairs of trominoes on an 8X8 grid

On an 8x8 grid I put 21 trominoes of thee different colors. Each group of 7 trominoes has one color. By visual inspection we see the trominoes cover the whole surface except the single empty square ...
1answer
245 views

### Stochastic Taxicab Path

A city's roadworks is laid out as a perfectly rectangular tiling. A commuter within this city has to travel to work a distance of 17 blocks east and 7 blocks north each day, and tries to take the same ...
3answers
288 views

### Optimal Strategy for Matching Pairs

I found a reality TV show recently that I thought would make a fun puzzle. On the show are 10 men and 10 women that have been "matched by experts" (ie. randomly paired). Their goal is to ...
1answer
143 views

### Self-intersecting polygonal chains in a hexagon [closed]

This is continuation of this Q&A. Given a regular hexagon with center at point O: Question: How many self-intersecting polygonal chains are there that connect 7 points? The self-intersecting ...
2answers
559 views

### Multiple of 3 in any numeric base

Can you find a positive binary number that is a multiple of 3 when it is read in any base from 2 to 10? A binary number contains only digits 0 and 1. For example the binary number "11" is 3 ...
2answers
826 views

### Frog game on a dandelion graph

There is some noise in the local pond. A group of frogs wants to host a birthday party! There is a total of 22 lily pads in the pond, each housing a single frog. They are labelled as numbers from 0 to ...
2answers
138 views

### Prime stepping stones

Start by placing number $1$ anywhere on an infinite square grid. Now place numbers $2, 3, 4, \ldots, K$ in order. A number $k$ can be placed if the following rules hold: It must be adjacent (...
1answer
144 views

### Sixteen cards on a table

Sixteen cards numbered 1 to 16 lay on a table. Anne and Clare each take four cards. Anne's cards add up to 23, while Clare's add up to 48. Bernard and David also take four cards each. The product of ...
1answer
73 views

1answer
181 views

### Elections in the United States of Alfagonia

Elections were held in the 45 electoral districts of the United States of Alfagonia. The Green Party won the election in 23 of the 45 districts. Alfagonia is made up of nine states of five districts, ...
1answer
228 views

### Equation $X^4-DY^4=Z^4$ (Part 1) [closed]

Let's have the positive integers X,Y,Z. The number D is a terminating decimal always. The numbers X,Y,Z do not have a common factor. Based on the above information, can you solve the following ...
4answers
237 views

### Addition table with hidden digits

Similar to the previous puzzle, find the values behind the letters. ...
2answers
393 views

### A fraction puzzle

This is a puzzle with both the computer-puzzle tag and the no-computers tag. We have the following list of five fractions: $$11/5, 30/77, 1/11, 21/2, 5/7.$$ Starting with an integer $x$, we perform ...
1answer
312 views

### Solving the equation X^4 - DY^4 = Z^4 [closed]

Let's have the equations $12^4 - DY^4 = 7^4$ and $24^4 - DY^4 = 19^4$. For what values of D and Y do these equations have a solution? Secondly, what little trick is required to obtain solutions of the ...
2answers
498 views

### What is the minimum number of problems in the pool? [closed]

Using a pool of problems, 16 tests will be formed, following certain conditions: Every test should have the same number of problems. Any problem should be included in at most 8 tests. Every group of ...
2answers
236 views

### The blind one who sees all

A blind prisoner is offered a deal by a king. 3 monks will be sent to his cell over a period of three days,only one monk will be sent to the prisoner's cell on any day. The king may decide to send one ...
2answers
199 views

### Simple math riddle with harvest workers

Some workers were assigned to harvest two fields, one of which was twice as large as the other. For half a day, the crew worked in the largest field. They were then divided into two equal groups. The ...
4answers
1k views

### Self-contained math crossword with if-then-else clues

An entry in Fortnightly Topic Challenge #43: Variety Crossword Grids Since I'm not good with with words and crosswords, here is a math crosswords: to know all the operands for the calculations you ...