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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14 votes
3 answers
2k views

Palindrome from the first 20 numbers

Can you concatenate the numbers from 1 to 20 in some order, such that the resulting 31-digit number is a palindrome? Bonus: if there are multiple such palindromes then what is the smallest one?
5 votes
2 answers
255 views

How do you produce the number 5, using only 3 eights?

How do you produce the number 5, using only 3 eights? The 4 operations (+ - x and division) + square root and factorial are allowed but no extra numbers (no squaring).
-1 votes
1 answer
143 views

How to arrange the colored cells in game grid?

Puzzle: In a game grid some cells are missing. Each line has only one colored cell with a label (a number greater than zero). This is an example grid and the number of columns/rows can be less than ...
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2 votes
1 answer
349 views

Probability that there will be no mutual best friendships? [closed]

Here is a problem: There are two groups of n users, 'A' and 'B'. Each user in A is friends with those in B, and vice versa. Each user in A will randomly choose a user in B as their best friend and ...
8 votes
1 answer
232 views

O princess, where art thou?

In the highest tower of her castle, a princess has N bedrooms which are arranged in a circle. She never sleeps in the same room on two consecutive days. Every morning she moves to another room by ...
6 votes
2 answers
225 views

Ernie and the Disguised Donors

I was spending the morning helping Ernie dig up the potato patch when he got an emergency phone call from the Society for Absent-Minded Mathematics Professors – it appeared that they had “A bit of a ...
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0 votes
0 answers
72 views

A house with 100 lights and 100 switches [duplicate]

There is a house with 100 lights. In the basement there are 100 switches for the lights. Sadly, you have forgotten which switch is connected to which light. Currently they are all on. You go down and ...
1 vote
1 answer
163 views

What are the exact times an analog clock with two identical hands and its vertically mirrored image show the same time?

Suppose you have a clock with two identical hands (there is no second hand). What are the exact times when this clock and its vertically mirrored image are identical?
2 votes
1 answer
260 views

What's the next term in this sequence?

I created this simple number sequence puzzle, I don't know if anyone used the same idea before. Find the term at the question mark in the sequence. $$ 25, 42, 56, 97, 176, 232, 251, 269, 394, 518, 572,...
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0 votes
1 answer
172 views

A simple number sequence puzzle

This is a simple number sequence puzzle, you are given 6 related number sequences, observe them, find the pattern; Your task is to give the first sixteen terms in the seventh sequence. $$1d5, 2d3, ...
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5 votes
2 answers
389 views

Determine the highest possible sum of all faces of cube

There is a non-negative integer written on all six faces of a cube. Integers on all possible three common adjacent faces (all faces are adjacent to each other) are multiplied and then they are added. ...
  • 1,095
4 votes
2 answers
799 views

Tic-Tac-Collatz

Have you ever heard of the Collatz conjecture? Just in case you haven't, I'll summarize it for you! Take any positive integer $n$, if it is even then simply divide it by $2$; however, if it is odd, ...
1 vote
2 answers
272 views

4x4 grid with the shortest longest path

This is an extension of this beautiful puzzle. This time your task is to find the hardest 4x4 grid. In particular, find a 4x4 grid containing every number from 0 to 9 at least once, such that the ...
6 votes
2 answers
506 views

Find out the longest path being alive [closed]

Start from any integer. Move horizontally or vertically (not diagonally), and if you come across the same integer more than once you will die. Moving diagonally is not allowed. What is the longest ...
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4 votes
2 answers
376 views

Can the Bomb squad succeed?

A bomb squad consisting of three members, person C had to defuse the bomb while other members (A,B) had the task to detect the bomb. The bomb squad was summoned to the bank to defuse 2 bombs located ...
  • 1,095
13 votes
2 answers
746 views

Only one such number exists

A 5 digit number ABCDE is divided by 2,3,4,5,6 and gives A,B,C,D,E as the remainders respectively. Can you find the only possible number? This was asked in my math exam, I think it would make a good ...
  • 1,095
11 votes
1 answer
321 views

Gah, these number sequences are just too boring!

Gah, these number sequences are just too boring! You just plug them in and then you're done! There is a function $f : \mathcal{S} \to \mathbb{Z}$, where $\mathcal{S}$ is a finite subset of the ...
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4 votes
1 answer
284 views

A prime time traveler

It is the year 2140 and you have just turned 40. After years of research, you have finally invented the time machine! It is a small device that fits in your pocket and allows you to travel in time. ...
15 votes
1 answer
804 views

Exterminating blobs on a grid

On an infinite square grid, some of the squares are occupied by little creatures called blobs. Cute as they are, it is your mission to exterminate all of them! You only have two methods at your ...
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10 votes
1 answer
431 views

How do you get the number

How do you use the format 1_*_ _ _ _ _ _ _ _ to get 222,222,222 using only the numbers 1-9 only once
  • 109
2 votes
0 answers
125 views

Maximize my flags - 2x2 version

Because Maximize my flags was not solved to optimality by the community, perhaps because the coding required was too harsh, I present you Maximize my four flags. The rules are exactly the same as in ...
  • 5,797
6 votes
4 answers
814 views

Paris and Wife Matchstick

Here are two matches dates that I hold with love in my heart: The current sum is 1970 + 1997 = 3967. You must requisition at most 10 matches so that the sum is "as big as possible". We will ...
  • 5,797
2 votes
2 answers
164 views

Prime sums in a 3x3 grid version 2

Can you place the first 9 natural numbers (1 to 9) in a 3x3 grid such that every row and column sums to a prime? The sums do not need to be distinct. Bonus: can you also make both diagonals sum to a ...
4 votes
2 answers
335 views

Prime sums in a 3x3 grid

Can you place the first 9 odd primes in a 3x3 grid such that every row, column and both diagonals sum to a prime? The sums do not need to be distinct.
2 votes
1 answer
192 views

Progressive Daedalian Opus

The 1990 Game Boy game Daedalian Opus is essentially a series of 36 pentomino puzzles. In the first level, however, you only have three pentominos; the rest are introduced in the levels after that, ...
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2 votes
1 answer
143 views

Alien decimal numeral system, part II

(continuation...) My alien friend said "do you think our system is strange? You need to have a look at our neighbour country, this is how they do it...", and then he showed me their ...
28 votes
1 answer
1k views

Alien decimal numeral system

During our travels around the galaxy we found many alien cultures with different number systems. However, this specific civilization was quite interesting: they had a decimal numeral system, just like ...
9 votes
1 answer
941 views

I can't remember her birthday!

My Persian friend said: I will meet you in New York on my birthday. But I can't remember her birthday! I only found this riddle related to her birthday in old chats. $(y+z)/y = (y)/z = (A+10)/10 $ $...
21 votes
3 answers
1k views

Complex Matchstick puzzle

This is my toughest invention so far, not sure if it's already been done but here it goes. Move a single stick to obtain a correct equality. (To be clear: the stick needs to be moved and placed down ...
0 votes
1 answer
384 views

Ivevihvw Zokszyvg Kfaaov

Vevib ovggvi szh yvvm ivkozxvw drgs gsv xliivhklmwrmt ovggvi rm gsv ivevihvw zokszyvg. Rh gsv mfnyvi lu ovggvih rm gsv zylev hvmgvmxv kirnv li xlnklhrgv?
5 votes
1 answer
274 views

Circle inscribed in triangle problem [closed]

You need to find the angle BEC knowing that the side BC is tangent to the circumference.
-5 votes
1 answer
149 views

The peculiar inequality

Let's have the following relation $\sqrt[3]{\frac{(x+1)^3+x^3}{2}}\lessgtr\frac{2x^2+2x+1}{2x+1}$ where $x$ a positive integer greater than zero. Which inequality is valid?
2 votes
2 answers
168 views

cheapskate jigsaw inc

Jigsaw puzzles are awesome and making them is an easy way to get rich. So I bought a cutting machine to make puzzles. Unfortunately I could only afford the cheapest machine available. All pieces are ...
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2 votes
1 answer
202 views

Something special about 2022-02-02

I was looking at the date today and it made me think of a mathematical object. Like March 14, which is known by some as as "Pi day". So the date is 2022-02-02. What mathematical object can ...
  • 22.5k
4 votes
2 answers
341 views

A simple guessing game

You and your friend play a simple guessing game. Your friend thinks of a secret whole number between 1 and 10, inclusive. If you ask your friend what the number is, the following happens: With 80% ...
5 votes
2 answers
326 views

Board game: Risk (two players)

Consider a game of two players: Player A and Player B. Each of them is assigned with the same number of soldiers. There is a battlefield (like a board game) with 7 tiles numbered 1 through 7 (a single ...
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1 vote
1 answer
144 views

Zettler's Encyclopedia

On epiphany 1735, Sir Zettler, who was a great publisher from the old continent, promised to issue a "Great Universal Encyclopedia of Collectible Wisdom". It was meant to be affordable for ...
7 votes
1 answer
1k views

Can you stop the falling piano with 23 nets?

MIT's Baker House has a tradition of dropping an irrepairable piano six floors every Drop Day, the last day one can drop a class without penalty (the 2022 date is 19 April). This year, in order to ...
  • 3,918
3 votes
1 answer
373 views

Two points inside a circle

Two points are randomly chosen inside a circle. Is it always possible to draw a straight line through each point, such that they subdivide the circle into 3 regions of equal area? Bonus: can the lines ...
-4 votes
1 answer
116 views

Why is the solution to this number table what it is?

I know the answer, but I have not yet discovered the path to the answer. Please explain why it is the answer.
6 votes
0 answers
371 views

Turn the dials until each of the 12 columns add up to 42

I received the wooden puzzle below for Christmas. After playing with it for a while I decided I needed to actually write something down if I was going to solve it. Eventually I just wrote an algorithm ...
  • 161
6 votes
1 answer
810 views

Binary Sudoku Puzzle

The rules of Binary Sudoku are quite simple. It is very similar to regular Sudoku, except here we try to fill a 9x9 board with only black and white tiles following the below rules: Every row, column, ...
5 votes
1 answer
1k views

Three lines to get twenty triangles

Shown below are five squares. Starting at any point, draw three straight lines without lifting the pen, and create exactly twenty (20) triangles. It is understood that this will create some other ...
  • 38.8k
8 votes
1 answer
291 views

Be Paired or Be Square

8 white and 8 black dots are drawn on a piece of paper. Parcly and Tori take turns drawing edges, always between white and black dots not already adjacent (so the graph is always bipartite); the first ...
  • 3,918
-4 votes
1 answer
127 views

Quantity expressed as the difference of two squares

What is the trick you need to use to be able to express the quantity $(4x^4+8x^3+7x^2+3x+\frac{1}{2})$ as the difference of two squares? addendum: The answer contains only rational numbers greater ...
12 votes
2 answers
751 views

An interesting geometry problem

I found this on the net and tried to solve it with no luck. However there is a tricky way of solving this problem and hence I am posting it here as a puzzle. Give it a try if you have not seen the ...
  • 38.8k
5 votes
2 answers
471 views

How many Wordle images are there?

Wordle (https://www.powerlanguage.co.uk/wordle/) has recently become a well-known word guessing game. The rules are simple: … a five-letter word is chosen that players aim to guess within six tries. ...
7 votes
2 answers
424 views

How many squares can a limp queen move to?

Consider a large chessboard. A limp rook is a chess piece that moves one step orthogonally, but it turns $90$ degrees after every move. The limp rook makes some moves, not crossing over its own path, ...
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6 votes
1 answer
319 views

The Resistor Game Show

You were one of $n$ contestants chosen to participate in a game show. Each of you will secretly select a resistor of your choice, with a resistance between 0.01 and 10,000,000 ohms. Once everyone has ...
10 votes
2 answers
529 views

Permutations of first 10 natural numbers such that all the prefix sums are distinct

I posted this question on Math SE as well. Did not receive any help. This is a question that I was asked in a Quant Interview. I would like you all to have a crack at this. I could not find a problem ...
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