# 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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114 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 (...
353 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 ...
326 views

### Dog's mead AKA The Little Pigley Farm

This is not a puzzle, this is a question about a certain puzzle, Dog's mead. Several forms of this puzzle have been known, and I'm referring to this particular form. There are some history on that ...
55 views

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### How many times does the earth rotate per year?

Assuming there are exactly 365 days per year, how many rotations about its axis does the earth make in one year?
193 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 ...
165 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, ...
69 views

### Date Validator Help Me plz [closed]

Mr. Bhola is not aware of Gregorian calendar dates. However, he knows that date is in the format ddmmyyyy. You need to draw a flowchart for Mr. Bhola which he can follow and determine whether a ...
413 views

### What is the minimum number of problems in the pool?

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 ...
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### Relations between numbers

Through some special formulas and relations I have come up with the following numbers 770, 84, 220, 6050, 1695, 29, 322, 45, 6095, 1666. How are these numbers related? Secondly, how were they ...
231 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 ...
214 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 ...
190 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 ...
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 ...
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 ...
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### Four equilateral triangles' areas sum to a fith

Let's have five equilateral triangles. From these five triangles one has an area equal to the sum of the other four triangles. All triangles have heights which are rational numbers. Can you find five ...
7k views

### Why is it impossible to connect 3 black dots to 3 red dots?

Connect each red circle with each black circle by drawing a line and the lines should not touch. From each red circle, 3 lines must be drawn which connect red circles with black circles, but the lines ...
1k views

### Ridiculous problem from an old maths textbook

There's a puzzling little problem I found in one of my old maths textbooks (Basics of Madthematics). In the middle of a whole bunch of normal problems on calculus and algebra and whatever, suddenly ...
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### After how many minutes will both hour hand and minute hand lie on one another

The following question was part of my mock test and I was unable to solve it. Assuming that: A: The hour hand and minute hand of the clock move without jerking B: The clock shows a time between 8 o'...
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### The tip of a colorful triangle

Original source: Problem 1 of British Informatics Olympiad 2017, Round 1 You're given a bunch of red (R), green (G), and blue (B) balls. I arrange some balls on a line. Then I ask you to complete the ...
358 views

### What is the missing value in this number pyramid?

The following question was asked in a mock test for which I am preparing and I was unable to solve it. What is the missing number? It must be one of these answers: A -19 B -5 C 9 D -9 The pattern I ...
157 views

### Four color a map - but go light on the fourth color!

Here's a map, which I found here: Your challenge is to four-color this map while minimizing your use of the fourth color. More specifically, color the map with four colors so each region is a ...
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### The Missing House Number

The Visit One day I was visiting my sister in Boston and heard a bunch of kids yelling and playing in the yard ( yahd ). I couldn't see the kids, and hadn't seen my sis for years so I asked her, "...
594 views

### Sum of digits of sum of digits of sum of digits

The following question was asked in a competitive exam for which I am preparing and I was unable to solve it (in fact I am completely clueless about it). So, I am asking for help here. Given a number ...
154 views

### My two button microwave

Long ago, I encountered a microwave with a display in the "HH:MM:SS" format. But instead of a number pad, you entered the desired time through two buttons: An "up" button, which ...
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### Numbers which use three times as many digits in base 2 as in base 10

Is there a largest number which uses precisely three times as many digits in its expression in base 2 as it does in base 10? Is there a largest number which uses precisely three times as many digits ...
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### 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 ...
162 views

### Consecutive numbers whose digital sum in base 10 is the same as in base 2

Find four consecutive positive integers each with digital sum in base 10 equal to its digital sum in base 2. Can five such numbers be found?
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### The children of the sultan

An old challenge from an old Portuguese book I have: Abdul Al-Kwaritz-Amuhmahd was a Arabic sultan who became very famous by the size of his harem and the number of children he had fathered. More so ...
346 views

### Maximize my flags

You are given the next list of 48 flags. For each pair of flags that are side by side, you score 1 point per color they share as a frontier. For instance France and Finland score 1 point thanks to ...
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### You surely don't want to score 100/100

The Story: Today, the Maths quizzes are handed out by the teacher. You got 100/100. Everyone got 100/100. But you're not happy with it. Everyone's not happy with it. You want to score lower. Everyone ...
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### Is it possible to put numbers and cut a hexagon? [closed]

You have numbers 1, 2, 3, 4, 5, and 6. It is required to put the numbers in triangles (one number in a triangle), so that when cutting a hexagon into two parts, the product of all the numbers in the ...
256 views

### Parallel Trees On The Grass

Let the picture speak for itself and try to find the correct height of the tree marked with "?". Hint Hint2 Strong hint
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### How do you find the sum of the digits contiguous to one which is situated in a three by three table?

The problem is as follows: I am placing the numbers from 1 to 9 in the squares of a 3 x 3 board. I start by placing the numbers 1, 2, 3 and 4 as shown in the figure. For the number 5, the sum of the ...
329 views

### Equilateral triangle inscribed in a square

A square is drawn on a piece of paper. How can you draw an equilateral triangle such that its vertices lie on the boundary of this square?
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### The unknown wheat-and-chessboard problem

You can read the original story of the Wheat and Chessboard problem on Wikipedia. (But you won't get anything useful from it :)) An eternity after the original ...
189 views

### The QWERTY-shortest word

For this puzzle, I define the distance between two letters as the shortest way on a QWERTY keyboard to go from a letter to another with a path. Examples: Q and W are seperated by a distance of 1. 2 ...
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### 7-QWERTY-distance words

My previous puzzle The QWERTY-shortest word was solved nearly instantly by the effective puzzling community. I also believe it is because the main parameter of the puzzle 4.7 was not perferectly set. ...
458 views

### Paying bills in Alphagonia

In the Kingdom of Alphagonia, where the national currency is the Alpha, banknotes are available in all whole-number denominations of alphas: 1, 2, 3,... a) What is the least number of such notes a ...
115 views

### Which step is creaky?

The problem is as follows: Ms. Flor has a 50-step wooden staircase that allows access from the first floor to the second floor. One of the steps creaks when a person stands on it. Diego and Mike are ...
A constant is hiding behind this puzzle, can you tell which? 4 $\rightarrow$ 2 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ $\dots$ ? $\rightarrow$ ? $\rightarrow$ ? $\rightarrow$ \$\...