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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2
votes
2answers
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 (...
11
votes
2answers
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 ...
7
votes
2answers
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 ...
-4
votes
1answer
55 views

More mysterious fractions [closed]

Let's have the following sums of fractions. $\frac{36020}{7203}+ \frac{36025}{7204}+ \frac{36030}{7205}+ \frac{36035}{7206}+ \frac{36040}{7207}+ \frac{36045}{7208}=F$ $\frac{15363}{5120}+ \frac{15366}{...
3
votes
1answer
112 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 ...
0
votes
4answers
223 views

Addition table with hidden digits

Similar to the previous puzzle, find the values behind the letters. ...
6
votes
10answers
463 views

Matchsticks 9 + 9 = 8 [closed]

You are given the wrong equation (made out of matchsticks) 9 + 9 = 8 and you can move at most 3 matches. Your aim is to find all possible correct equations. Selected answer will be one that discovers ...
9
votes
3answers
571 views

Find the next term of $\frac14,1,\frac94,2+\frac2{\sqrt{3}}, \frac{5}{2} + \frac{5}{2 \sqrt{2}}, 3 + 3 \sqrt{\frac{1}{10} (5 + \sqrt{5})}$

You are given the sequence: $$\frac{1}{4}, 1, \frac{9}{4}, 2 + \frac{2}{\sqrt{3}}, \frac{5}{2} + \frac{5}{2 \sqrt{2}}, 3 + 3 \sqrt{\frac{1}{10} (5 + \sqrt{5})}$$ Transcription: one fourth, then one, ...
-4
votes
1answer
84 views

Use only πs to get e

I am taking this puzzle from inspiration from the Four Fours to get Pi puzzle. The puzzle rules are just slightly different. Here are the rules: You are trying to get as close to e as possible with ...
1
vote
0answers
145 views

Robot's Step, Step, Sent Back!

So there is this robot. Its origin is at (0, 0), index 0. Each pair of coordinates will have same numbers for x and y. How the robot moves is this: (0, 0) index 0, (1, 1) index 1, (1, 1) index 2, (2, ...
-1
votes
2answers
79 views

How many sticks to make a grid of squares? [closed]

We can arrange short sticks to make grid of squares, as in the 3 x 3 example of the figure below, which requires 24 sticks. How many sticks are required to make a 151 x 143 grid of squares?
1
vote
1answer
120 views

The mysterious fractions

Let's have the following fractions. $ \frac{752}{375} + \frac{754}{376}+ \frac{756}{377} + \frac{758}{378}+ \frac{760}{379} \approx 10\times(\frac{5}{375}+1)^{1/5}$ $\frac{752}{375}+ \frac{754}{376}+ \...
9
votes
2answers
761 views

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?
-14
votes
1answer
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 ...
-5
votes
1answer
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, ...
-5
votes
0answers
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 ...
9
votes
2answers
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 ...
0
votes
0answers
96 views

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 ...
-14
votes
1answer
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 ...
-1
votes
2answers
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 ...
4
votes
2answers
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 ...
32
votes
2answers
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 ...
33
votes
2answers
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 ...
-4
votes
1answer
88 views

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 ...
34
votes
7answers
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 ...
38
votes
1answer
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 ...
3
votes
4answers
133 views

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'...
13
votes
1answer
521 views

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 ...
6
votes
3answers
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 ...
7
votes
1answer
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 ...
2
votes
3answers
414 views

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, "...
6
votes
4answers
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 ...
7
votes
1answer
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 ...
5
votes
3answers
792 views

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 ...
73
votes
15answers
80k 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 ...
5
votes
2answers
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?
5
votes
2answers
201 views

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 ...
9
votes
2answers
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 ...
20
votes
3answers
5k views

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 ...
-4
votes
1answer
69 views

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 ...
4
votes
0answers
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
1
vote
1answer
94 views

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 ...
10
votes
1answer
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?
1
vote
1answer
86 views

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 ...
5
votes
1answer
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 ...
6
votes
1answer
178 views

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. ...
5
votes
2answers
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 ...
2
votes
1answer
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 ...
5
votes
1answer
355 views

Some mathematical magic

The magician will perform some mathematical magic. He asks his guest to secretly pick any two digit number and then perform a number of operations on it. If the number is even, divide by 2, if it is ...
4
votes
1answer
125 views

Constant puzzle

A constant is hiding behind this puzzle, can you tell which? 4 $\rightarrow$ 2 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ $\dots$ ? $\rightarrow$ ? $\rightarrow$ ? $\rightarrow$ $\...

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