Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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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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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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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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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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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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2answers
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Coin weighing problem

You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision. You know that all stacks of coins are made from gold, weighing 10 grams per ...
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1answer
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What did I do yesterday Rebus?

What did I do yesterday ? Above image is the rebus. Src : slightly copied .
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8answers
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Is this 10-card magic trick possible?

A magician (Yes, that's you) has 10 cards, say labelled 0 to 9. Now, the magician's assistant and the magician perform a magic trick: The magician turns around (so he can't see the cards) A volunteer ...
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2answers
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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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2answers
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SPEND LESS MONEY alphametic

The well-known verbal arithmetic problem S E N D + M O R E ----------- M O N E Y explains (or at least it did the first time I knew about it) the story ...
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3answers
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A smudge in his notebook

Lothar took his notebook and started scribbling some equations: \begin{align} 2 + 3&= 412 \\ 1+5& = 4321\\ 0+4&=4320\\ 4320-412&=40\\ 4321120-0&=3\\ 80-62&=0\\ 6+6&=\text{■...
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Strategy to beat the casino over the long haul

$A$ and $B$ are attempting to beat the casino again, and the rules are the same: Each round, $A$, $B$, and the casino simultaneously decide to show a $0$ or a $1$. If all three numbers match, $A$ ...
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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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17answers
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Number 88 from the digits 2, 0, 1 and 7?

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?
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26answers
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Building a 2 mile runway on a 1x1 mile island [closed]

You have a 1-mile long x 1-mile wide island. When taking off from a flat runway, a plane requires a runway of minimum length 2 ...
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6answers
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How many digits can you create with only one seven segment display?

Let say you have a digital indicator which consists of seven lights as you see below. You are trying to make as many distinct digits as possible but there are two requirements for that: At least one ...
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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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7answers
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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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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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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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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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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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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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6answers
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My Sixteen Friendly Students

I have sixteen students in my class who sit in four rows of four. Each week they sit in a different order. After a number of weeks every student has sat next to every other student, next meaning ...
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4answers
2k views

Obtain the “Master of stones” title

Note : the mechanisms described in this puzzle are related to those found in this question. This is a game of 2 players. Each player can pick up 1, 2, or 3 coins in any pile (copper , silver , gold) ...
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2answers
2k views

“Legally” filling a 10x10 table with 10 of each digit

Professor Halfbrain has spent his entire weekend by filling $10\times10$ tables with the digits $0,1,2,3,4,5,6,7,8,9$ so that each digit occurs exactly $10$ times. According to the professor, such ...
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2answers
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prove that 2016 is a self-composable number

Define a number self-composable if it may be computed using just the digits of the number itself (used just once) and the following operations: basic operations ( $+, -, \times, \div$) less than ...
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4answers
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How many boxes are conductors?

The Question (Some knowledge of potential difference, resistor combinations, etc. required) You have 1000 boxes. Some (or none) of them are conductors (of negligible resistance). The rest are ...
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1answer
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Mystery operation

In a future not so far way, Earth archaeologists find on a far away planet a fragment from a long lost civilization. This fragment involves an unknown operation *|*...
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2answers
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Ernie and the Alien Invasion

Yesterday I dropped in on Ernie to show off my new j-watch. Ernie wouldn't be impressed by instant wrist-mounted access to social media sites like me-tube, tweeter and farce-book so I thought I would ...
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4answers
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Magician's hide and seek with 8 cards

This question is a followup to this question by @Wen1now. After demonstrating the previous trick, the magician decided to make things a bit harder, discarding some cards so that only eight were left. ...
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4answers
761 views

Ernie and the Uneconomical Flat-breads

When I arrived at Ernie's place last weekend I had some exciting news for him. "did you know", I announced "that a new Kzijekistanian fast-food shop has just opened in town?". "I did", Ernie replied, "...
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2answers
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Diet Coke or water?

At PuzzlingCorp, all employees have a break at 10:00am sharp every day, and immediately proceed to get either plain water or a diet coke. The people at PuzzlingCorp are also highly susceptible to ...
19
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1answer
427 views

Filling a 13-by-13 square

Is it possible to arrange the integers $1,2,3,\ldots,169$ in a $13\times13$ square, so that in every $2\times2$ square the sum of the four numbers is divisible by $170$?
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Which is larger? $\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2}$ versus $5$

Which side is larger? $$ \sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2} \stackrel{?}{\lessgtr} 5 $$ Without using a calculator, computer, or estimating square roots, please determine which side has the ...
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5answers
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How to get 5 from 0,0,0 and 1?

Can you use the digits 0,0,0 and 1 each only once in a mathematical expression for the number 5 using only common mathematical symbols with at least 1 mathematical symbol between each number?
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5answers
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Divide an integer by 2 by replacing 9 with 0

What are examples of integers that halve their values when all 9's in their decimal representations are replaced with 0's?
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9answers
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One-one communication

5 people are standing in a circle - person A needs to tell his salary to person B, but none of the others should know A's salary. How is this possible, if every person only whispers to the person on ...
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6answers
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How Can I Safely Double The Length of A Ladder?

I'm posting this from the roof of a building because I can't figure out a safe way down. I've scoured the roof for anything useful, and all I found was a coping saw. I also found a 100 foot ladder, ...
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3answers
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Math with dinosaurs

Doctor Brun was at it for years, but he'd finally got his time machine up and running. His first trip was to a time way back in the past when dinosaurs roamed the Earth. To his surprise, the dinosaurs ...
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2answers
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Blackboard cleaning

The blackboard contains 30 integer numbers from 1..2000. Each minute you are allowed to elect some positive integer number x and subtract x from some (chosen by you) of the numbers on the blackboard ...
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6answers
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Guess five binary digits!

Person A thinks of a 5 digit binary number. Person B tries to guess the number. B can guess a 5 digit binary number and A will respond with the number of correct digits (digits in the right place). ...
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3answers
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Tiling a rectangle with nine squares

A rectangle is tiled by nine squares with side lengths $2,5,7,9,16,25,28,33$ and $36$ (without overlapping and without gaps). What are the side lengths of the rectangle? What does the tiling look ...
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2answers
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We are two immediate neighbors who forged our own powers to form concatenated relationship. Who are we?

Our concatenated number is $ \overline{ABAC}, $ where $ A, B, C $ are all positive digits (1 - 9). Our relationship is $$ \overline{ABAC} = A^A + B^B + A^A + C^C $$ Who are we?
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What is special about this grid?

Here is a simple grid with letters in them? There is one significant word and ten special numbers in it. Four questions: What is the significant word? What are the ten special numbers contained in ...
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3answers
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Professor Halfbrain and numbers with many zeros

Yesterday I met professor Halfbrain at the opera. During the break, the professor told me that he has made the following amazing discovery: Professor Halfbrain's theorem: With a finite number of ...
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1answer
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How does this addition work (13+7=1130)?

I found this problem on 9gag and I have no idea how to solve it. Here is the question: $13+7=1130$ $88+9=47$ $32+28=2530$ $10+999=1149$ $444+77=61$ $55+111=56$ $21+0=1221$ $7+22=39$ $33+5=38$...