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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The LoL number game

Tim and Tom are fictional characters (cats, I believe) who like to play the LoL number game. In this game, Tim chooses two distinct integers A and B, both ≥ 2, and shows them to Tom. Tom's goal is to ...
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478 views

Dominoroto-toto

Consider a domino tiling of a plane rectangle of size $n \times m$. (Obviously, at least one of $m$ and $n$ has to be even for that to be possible.) I personally hate those because they tend to look ...
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The Faulty Keypad Safe

Acme has released a brand new safe, secured with electronic 10-button keypad with the digits 0 through 9, with an X-length combination required to unlock. However, due to laziness, the keypad's ...
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3answers
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3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
22
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1answer
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A few Mathematicians derived from formulae

Find the 3 mathematicians which may be revealed, with a little manipulation, from the formulae below. They are well known enough to be in the MacTutor History of Mathematics archive. $$\frac{\chi }{...
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4answers
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Ernie's Clockwork Calculator

I was helping Ernie clean out his shed a while back when I saw a curious old machine. "Oh yeah, that!" said Ernie, when I pointed it out to him. "A few years back, before transistors were invented, I ...
22
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2answers
773 views

The answers to these questions are?

C is the correct answer to how many questions? A. 1 B. 2 C. 3 D. 4 Which letter is the correct answer fewer times than any other? A. D B. B C. C D. A Which letter is the ...
22
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1answer
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Monte Carlo Chess

This is an entry to the 17th fortnightly topic challenge. Chess is an interesting game, but is so unrealistic. In real life, you couldn't tell order your knight to attack an enemy bishop and expect ...
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10answers
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Five Angles in a Star

In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following? Now the ...
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6answers
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What world is this where 6 + 6 = 10?

Upon traveling the world, I found myself in a peculiar place which was called Gauss. The locals there were a peculiar people, as I soon found out. I stopped to grab a bite to eat and learn about the ...
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Picking up stones

Here is puzzle that was lifted from an old essay of mine, that was adapted from a puzzle in an old puzzle book. The great shah has invited a young boy into his palace as a student. While he is not ...
21
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4answers
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Hidden in plain sight - By what method do these images hide a prime number?

Note: This question has been severely edited from its original version to better fit the format of this site. Some answers below - including the accepted, correct answer - have been given based on the ...
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8answers
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Robots in a spaceship

Xerxes has 6, 7 and 8-arm robots in his spaceship. Unfortunately, the 7-arm robots are misprogrammed and everything they say is a lie. The other robots are fine, they always speak the truth. Once ...
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2answers
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Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
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4answers
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What's in my pocket?

Well, I can tell you Johnny has memory cards in his pocket. Back Story My brother, Johnny, is a tech nerd. He loves gadgets of all kinds. As a matter of fact, you can be sure at any one given time, he ...
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Reach the Maximum by Flooring It

A nice easy puzzle for the math lovers out there. We're all familiar with the $\max$ function: $$\max \left( {x,y} \right) \triangleq \left\{ {\begin{array}{*{20}{l}} x&{{\text{if }}x \geq y} \\...
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3answers
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Ten Tricky Mathematicians

Somewhere on the Hyperbolic Plane, you encounter ten mathematicians. You know that some of them always tell the truth while the rest always lie. Each of them knows which of the others tell the truth ...
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A Bridge Problem

You are on the North Shore of a river, and you want to get to the South Shore. In the river are 6 islands and 13 bridges connecting the islands and shores. However, a storm gives a 50% chance to each ...
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Checkerboard Infection: The Aftermath

As in this previous puzzle, we are again playing with our favorite bacteria, C. Coli, whose natural habitat is an 8x8 checkers board. These are very nasty bacteria - once they are in a cell of a ...
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6answers
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3x3 “Magic Square” of Prime Numbers

During the thinking and analysis of some mathematical problems, I came up with this puzzle: Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
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3answers
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N pirates steal their share of bananas to the benefit of a monkey

The following is a type of logic / math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. $N$ pirates find themselves ...
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Concatenation divisible by 19

You are given a 9-digit number $a$. Let $b=a+1$. Now, if you make a big number $N$ by concatenating $a$ and $b$, then $N$ is divisible by 19. What is the number $a$?
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Winning an unfair game

I came across the following interesting problem today: A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability $p < \frac{1}{2}$, he ...
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4answers
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Infinitely many dwarves wearing hats of 2 colours

I have heard of the puzzle with 100 or 10 dwarves wearing a hat of a color, either red or blue, and standing in a straight line, and having to guess the color of their own hat - it's quite easy. The ...
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1answer
651 views

A table filled with greatest common divisors

Yesterday I met professor Halfbrain at an art gallery. The professor told me that recently he had been spending his time with constructing $n\times n$ tables for integers $n\ge3$: the entry at the ...
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1answer
521 views

From zero to parabola in 14 symbols

Post up, weekend analytic geometers, get ready to race for the parabola and approach the starting line with 0 and 7 other symbols:       0   =   ( ...
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1answer
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Orange you glad it's not Lemon?

My friend gave me this note in class, my very own third grade mathematics class! But alas: To little, my third grade-ly efforts amassed. Again and again, I wish I'd known then,...
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Master Bomb Defusers

Day 115 of your investigation and you and your ever-faithful-if-only-a-bit-slow partner have finally caught the trail of your arch-nemesis, a serial bomber known only as "Mr. 5". Doing your ...
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12answers
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What's the largest number you can spell?

If I give you one of each letter in the alphabet what's the largest you can spell (in word form)? Bonus: What's the smallest? Bonus 2: What if you can use the words "minus", "plus" and "times"?
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Size of a square in a square

Given a unit square (blue in the picture), pick a point on one edge and label it A. Label the distance from the nearest corner to A as x. Pick one of the corners opposite A and label it B. Call the ...
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9answers
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Simple Maths Riddle 2

I have a definition, but I'm not literally defined. The simplest of shapes: circles and lines. A decimal you'll require; my anagram leads a choir. What am I? HINT 1
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3answers
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What is my real name?

My Father is a Chemist My Mother is a Mathematician They call me iron59 What is my real name?
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A tale of The Rich Arab man

A tale of The Rich Arab man. There was a rich Arab man who had four wives. One day he decided to give away all his diamonds to all of his wives. He carried all his diamonds in a huge bag, walked ...
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4answers
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Mutilated chessboard

Remove the square in the top-left corner of a $2015 \times2015$ chessboard. Can the remaining mutilated chessboard be tiled with $1\times4$ and $4\times1$ rectangles?
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Order order everywhere

Something strange happened yesterday night. It is about a chain of images that I saw while sleeping, in dreams. The following are the sequences I saw: At 1 am, ...
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11answers
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Add parentheses to make this true

Add parentheses to the following to make a true equation: $10-9\times8-7\times6-5\times4-3\times2-2\times1=1$
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10answers
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Creating 2020 in the fewest number of steps

You start with the number 1. You can create a new number by applying an operation on two existing numbers (can be the same). The operations are +, - and *. What is the fewest number of steps needed to ...
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5answers
915 views

Professor Halfbrain and the powers of 2016

Yesterday I met professor Halfbrain at the coffee house. The professor told me that he had been spending his time with computing powers of $2016$ and combining them with powers of $32$. The professor ...
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3answers
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A chess board with numbers

A 8x8 chess board is marked with the numbers from 1 to 64 sequentially from left to right, row by row and top to bottom. Now a minus sign is added to 32 of those numbers such that in each row and in ...
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4answers
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The frog concerto

A pond contains $24$ waterlilies that are arranged in a rectangular $2\times12$ grid (that is, two rows with twelve waterlilies). One evening $24$ frogs give a croaking concerto for the residents of ...
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1answer
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Is it possible to divide a square into convex pentagons?

I have seen this question on reddit (r/math's chatroom - to be specific). No one has answered it yet, so I thought I would pose the same question here. The only discovery I made that is worth ...
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1answer
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Dominos on a checkerboard

What's the maximal number of dominos (2x1 tiles) that can be placed on a checkerboard (8x8 square) so that every domino covers exactly 2 squares of the checkerboard and no two dominos form a 2x2 ...
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6answers
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Trapped in my Cellar

I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
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1answer
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It's my weird friend

My weird friend is back. He asked me to guess a number. Then instead of waiting for me to guess like a normal person, he handed me a piece of paper with this written on it: You thought this clue ...
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6answers
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The Unfinished Puzzle Section

Simply complete the sudoku and crossword, happy puzzling. Across 1. Achieved acclaim by being knowledgable about strange apron (3, 6) Down 2. Explode asteroid five to refrain from inactivity or ...
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3answers
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The mysterious card in the middle

The referee tells Lefty, Righty, and Middly: "I have picked three positive integers $L,M,R$ with $L<M<R$ and $L+M+R=13$, and I have written these numbers onto the three cards lying face down on ...
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7answers
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Ali Baba and the 10 thieves

EDIT: This puzzle originates from the "International Mathematics Tournament of the Towns", and was published in the book "S.M.A.R.T circle overview" by Professor Andy Liu. The author has (albeit a ...
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4answers
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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 ...
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3answers
621 views

Filling the plane with two colors

In this puzzle you must tile the plane with colored T-tetraminos. I will start by laying down 3 of them for you like so: Your task will be to tile the entire rest of the plane meeting the following ...
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3answers
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An arithmetic puzzle from 1645

The following problem is found in the first Norwegian arithmetic, published in 1645 by Tyge Hansøn: Three hundred oxen large and small, A cattle owner wanted to buy: 3 for 63 daler he got. ...

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