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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4
votes
3answers
320 views

Scientifically Themed Rebus/Dingbats - Part 3

The same idea as before: the "scientific" expressions represent some form of popular media. Enjoy. Part 1 Part 2
12
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1answer
1k views

222 x 555 = hill

When I multiply numbers that contain twos and fives, I get a number, the digits in which first increase and then decrease, for example: ...
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1answer
88 views

A question based on cutting a wire to form a tetrahedron

I am trying exercises of Quantitative Aptitude and I am unable to work out how this problem can be solved: As a tetrahedron has 6 edges, I thought 5 cuts should be required. But that's wrong. Answer ...
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2answers
2k views

A puzzle question asked in mathematics exam

I am self studying for an exam and I am unable to solve this quiz question. I tried to find the numbers in the sentences but I couldn't find them and I think that's a wrong approach. Can anyone ...
7
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1answer
861 views

Unable to solve a question asking to find the missing number in sequence

I am trying some quantitative aptitude questions and I am unable to solve this particular question: Unfortunately, I have no clue how it can be solved; I am not able to start. However, I know the ...
6
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1answer
222 views

Question which is sort of puzzle from mathematics Exam

I am self studying and trying questions of quantitative aptitude in my mathematics exam and I am unable to solve this problem. Of three persons $A$, $B$ and $C$, one always lies while the others ...
14
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1answer
590 views

The numbers on blackboard

The numbers $2020,2019,2018,...,1$ are written on the blackboard from left to right. John repeats the following process until there is only one number left: John chooses the first two numbers from ...
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1answer
253 views

Math tapestry puzzle #3

Continuation from Math tapestry puzzle #2 Now things are heating up, it looks like this is slowly becoming bigger. I saw my friend Anna working on her tapestry. She asks me, "Do you like it?"...
5
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2answers
178 views

Swapping the first and last digits of an integer

Take any n-digit integer (n > 1) and interchange its first and last digits. If neither of these is 0, and they are different, does it happen infinitely often that the resulting number is a multiple ...
4
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1answer
232 views

What is the maximum length of sequence where the sum of 5 consecutive numbers in positive and sum of 8 consecutive numbers is negatve

What can be maximum length of such sequence? Hint one such sequence is
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1answer
96 views

Find the unique passcode

"Is this the Coldport Lost Property Office? I think I left my puzzle-book on the train this morning, and I was hoping someone had handed it in." The speaker was a tall gentleman with a six-...
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4answers
402 views

All wrapped in functions

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(x)f\big(f(x)+y\big)=f\big(x^2\big)+f(xy)$$ for all $x,y\in\mathbb R$ Problem by me Most elegant solution wins!
5
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4answers
356 views

Complete this cross sequence

What is the next element of this sequence and why? Possible choices: Hint 1 Hint 2 Hint 3 Hint 4 Hint 5
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2answers
161 views

Missing number in a set of four segment circles

This is a puzzle posted on a social networking site that I have been trying hard since yesterday to solve: My approach has been to find out a mathematical function with the numbers in the yellow, ...
3
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1answer
196 views

Is this Series limited to six numbers only?

May be this problem is already answered. I am not aware. What is the next number in the following series? Importantly, after that number, are there any more numbers? is there a math related reason for ...
7
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2answers
625 views

Lock Optimisation

In a simple combination lock, a sequence of several digits is used as a password, with one wheel per digit. Generally, it is not possible to unlock the lock without knowing the password, but due to ...
14
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3answers
314 views

Cryptic Crossword?

You pick up a discarded newspaper, hoping to satiate your need for puzzles with a cryptic crossword. But as you turn to the page, you feel something is awry – perhaps some elision? Across 3. $F_6,F_7,...
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4answers
2k views

Boys and girls in a circle

There are $28$ students in a class, and each of them are either boy or girl. They sit in a circle, and claim that “The two people next to me are of different gender than each other.” It's known that ...
2
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1answer
94 views

Calculation puzzle 006

Find the number which corresponds to the place indicated by the question mark. ...
3
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3answers
120 views

finding a number using clues [closed]

The digit on hundreds place of a three-digit number is 2, the digit on tens place is 3 less than the digit on ones place. 6 times the product of the three digits is 20 less than this number. What is ...
3
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2answers
220 views

Cannonballs packing

A pile of cannonballs stacked like a pyramid has a rectangular base. Each layer has a length and a width in terms of cannonballs that are each one less than those of the layer that is directly below. ...
6
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1answer
287 views

Scientifically Themed Rebus/Dingbat Puzzles - Part 2

below are more rebuses with "scientific" expressions that represent something in popular media. Part 1 here. One of the questions in Part 1 has a link to a question here.
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0answers
891 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 ...
31
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3answers
2k views

Knights on a Torus

An 8×8 chessboard is in the shape of a torus. (This means that the board "wraps around" - you can go left from a2 and come out on h2, for instance. It also works vertically - you can go up from f8 and ...
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4answers
804 views

Scientifically Themed Rebus/Dingbat Puzzles

Below I have created a list of a few "scientific" expressions that represent some form of popular media, with the type stated. Hope you enjoy.
6
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2answers
771 views

Exam statistics

250 teenagers gather for an exam. Peeking at the roll, a math-inclined among them note that if they are split into 10 groups of 25 per alphabetical order, then in each group, there are two with the ...
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3answers
247 views

Find a good strategy to survive the multiplayer duel

Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
3
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1answer
167 views

Calculation puzzle 005

396 ? 556 99 872 664 I tried to solve it but to no avail. Possible answers are 666, 491, 654, 999 and 917; since, the exam was multiple choice we were ...
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3answers
2k views

1 in, 1 out (The Security to the Party Maze)

A party is being held at a local mansion. The host is very rich and his success is because of one thing ~ his famous recipe for spaghetti! The spaghetti recipe is kept in a secret room inside the ...
5
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2answers
259 views

What should you substitute?

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$xf(x)-yf(y)=(x-y)f(x+y)$$ for all $x,y\in\mathbb{R}$. Problem by me. Most elegant solution gets the checkmark!
3
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1answer
207 views

Find the equation of this surface - The Snowman

Here is a surface that resembles a snowman: Its equation has the form $f(x,y,z)=0$: if a point $(x,y,z)$ satisfies that equations it is shaded, otherwise it is "left blank". Your goal is to find $f$. ...
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2answers
255 views

Fibonacci progression

In a number sequence, 1, 13, 169 and 2014 are respectively the first four terms of the sequence. The next terms are equal to the sum of the four numbers that precede them. For example, the fifth term ...
25
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1answer
802 views

An Evolutionary Experiment

Dr. Farnsworth entered class today and announced that we were going to conduct an experiment to see if we could force cells to evolve to communicate with us. The experiment is as follows: we are given ...
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5answers
2k views

Maximise your gold!

You met a genie. He gets $150$ magic lamps out, which are numbered from $1$ to $150$. You have to colour each lamp red or blue. After colouring, the genie will count the number of triples $T$ of magic ...
13
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8answers
2k views

n(n+1) as a multiple of 100

Here's a puzzle I came up with while walking today: For how many natural numbers $n$ is the number $n(n+1)$ a multiple of $100$? This is true for infinitely many $n$, so "how many" means something ...
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3answers
3k views

Lottery strategy

In a city, the official lottery consists of scratch cards that cost 10 bucks each. Each scratch card contains 36 squares with a hidden number on each square : 21 of them are “zeroes”, 9 of them are “...
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2answers
595 views

Sort 9 train cars on 3 paths

On the three paths of a station are A, B, and C types of train cars as shown in the figure. A locomotive driver (L) can attach from 1 to 9 train cars to a locomotive at any time, move them to the ...
12
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0answers
269 views

A fairy tale in a golden toy

Once upon a time, long long ago, in the days when good stories were far more beautiful and far harder to come by, a king was asked by his spoilt but beloved princess daughter to give her a fairy tale. ...
8
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3answers
578 views

In honour to 2004

222444 is the smallest number that is divisible by 2004 and only contains the digits 2 and 4. What’s the next number that has the same properties? Hint:The number is 11 digits long.
12
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1answer
812 views

Functional equation by me!

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(x)f(x+y)=xf(x)+f\big(f(x)\big)f(y)$$ for all $x,y\in\mathbb R$. Source: Problem by me.
4
votes
1answer
121 views

Kings on a chessboard

Let $n$ be a positive integer. You are given $4n^2$ kings and a $4n\times4n$ chessboard. You have to place the kings on the chessboard such that each row and column contains exactly $n$ kings, and no ...
6
votes
4answers
668 views

Numbers that are the sum of the cubes of their digits

There are just four 3-digit numbers which are the sums of the cubes of their digits. For example: $370 = 3^3 + 7^3 + 0^3$ and $371 = 3^3 + 7^3 + 1^3$. Without using a calculator/computer, can you ...
3
votes
1answer
74 views

Multiples of their reversals

8712 and 9801 are the only 4-digit numbers which are multiples of their reversals: 8712 = 4*2178 and 9801 = 9*1089. Without using a calculator/computer, can you find two 5-digit numbers with this ...
9
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1answer
217 views

Mathematical golfing

You have probably heard of code golfing? There the task is to find the shortest computer program that produces the required output. Here we want to perform math golfing - find the shortest formula ...
8
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2answers
831 views

Wait, it is worth it?

You went to a Casino, and saw a quite interesting stall. The cardboard besides the stall says: You first pay \$$5$ You have to toss the fair coin. If it lands heads, you can ...
9
votes
1answer
348 views

A functional equation again!

Determine all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$(x-2)f(y)+f\big(y+2f(x)\big)=f\big(x+yf(x)\big)$$ for all $x,y\in\mathbb{R}$. Source: Math Excalibur Volume 22, Number 1 ...
10
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4answers
469 views

Floor functional equation

Find all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying the following functional equation: $$f(\lfloor x\rfloor y)=f(x)\lfloor f(y)\rfloor\quad\quad\text{for all }x,y\in\mathbb{R},$$ where $\lfloor\...
3
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2answers
106 views

Tangential circles

The following figure has two axes of symmetry which define its width and length. The length (horizontal distance) is twice the width (vertical distance). The largest circle has a radius of 2005 and ...
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7answers
6k views

9-5=5? Matchstick problem

Move one matchstick to make an equality. Question made by me (Is this too easy?)
9
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2answers
279 views

Probability of picking the red marble twice

Start with a bag containing one red marble and one white marble. Reach into the bag and pull out a marble at random. Put it back and do it again. If, on both times, you grabbed the red marble, stop. ...

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