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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I'm largest when I'm five, what am I?

I'm very common and often you see me, Everything's believed to be made of me. Make no mistake, I look largest when I'm seven, But I'm largest when I'm five, it is proven. But alas at ...
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Chasing pirates

You are asleep on your boat on open sea. When you wake up you discover you have been robbed. A quick inspection of security cam footage reveals that the pirates who robbed you left your ship exactly ...
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Measure 22 minutes with 7 and 13 minute hourglasses

You have two hourglass timers. One can measure 7 minutes and the other hourglass timer can measure 13 minutes. This means that it takes 7 minutes for the sand timer to completely empty the sand from ...
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Unsolved Maths Problems as Puzzles

On an internal wiki at work, people sometime post puzzles similar to those found on this website. Most of the questions are formulated as a story or word problems, but can be expressed mathematically ...
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A Surprising Circle Packing

A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, ...
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Filling an 11-by-11 square

Is it possible to fill the $121$ entries in an $11\times11$ square with the values $0,+1,-1$, so that the row sums and column sums are $22$ distinct numbers?
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The subtraction game

Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. Every number can be picked ...
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Strategy to beat the Casino

Two players, $A$ and $B$, and the Casino play a game. It involves showing zeros or ones: each player picks $0/1$ and also the Casino picks $0/1$. If the Casino and both players $A$ and $B$ show the ...
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Ernie's automatic parking valet

I was helping Ernie out in his shed a while back, when his favorite screwdriver suddenly wore out. I offered to go and pick up a new one for him and Ernie thought it was a great opportunity to test-...
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Ten girls around a table

Ten girls are sitting around a table. Each of them picks a real number and whispers it to the two neighbors immediately to the left and to the right. (Hence: each girl communicates one number, and ...
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Can political debates really work?

In the far-off country of Politica, there are three main parties: the Left, the Right, and the Centre. In the last election, there were 19 million Left voters, 21 million Right voters, and 23 million ...
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What bases make this number square?

For what values of $x$ is the number $121$ a square in base $x$? This is a very easy question, but I still think it's pretty fun. Perhaps it's something to pass on to younger people who are taking ...
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Cut the disk with a hole in four equal pieces

Cut the shape below in four congruent pieces. The gray area is a hole. In non-mathematical terms, cut the white area in 4 pieces having the same shape, same size, possibly mirrored or rotated. Note:...
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Will the ant reach the car?

A car starts distance 1 from a wall then drives away at constant speed $c$. There is a length of elastic tied between the wall and the car. Remarkably this doesn't affect the motion of the car (in ...
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Honest Monk Puzzle

Suppose you are on an island with 32 monks and you are told that one of the monks is always honest. Every day the monks say whether it is going to rain. You are required to say whether it is going to ...
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The Devil's Brother

The 1933 movie "The Devil's Brother" (also known under the title "Fra Diavolo") takes place in the Northern Italy of the early 18th century. Stan Laurel and Oliver Hardy play the fierce robbers ...
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Variant of lion and 100 zebras

Note: This problem remains unsolved, as of 4 Feb 2018, so do try it out This a variation of this question by @Gamow Suppose there are $100$ lions and $100$ zebras. The lions function together as a ...
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How many cars does the millionaire have?

I had a logical riddle on a programming interview test which was something like this: In his garage a millionaire had cars, of which only 2 were not white, only 2 were not green and only 2 were not ...
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Happy pi day, everyone!

A baker is working a batch of dough. He shapes it into a cylinder of height a and radius z. What will the baker make from this volume of dough?
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Who drinks beer while running anyway?

A variant (I don't have the book in front of me, so this is a paraphrase) of this puzzle was in the book Brainteasers and Mindbenders, by Robert Hamilton. It has stuck in my mind since I read it in ...
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The ping pong puzzle

Three friends ($A$, $B$ and $C$) are playing ping pong. They play the usual way: two play at a time, the winner stays on, and the loser waits his/her turn again. At the end of the day, they summarise ...
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Professor Halfbrain and the sum of the digits of all divisors

Yesterday I met professor Halfbrain in the city. The professor looked tired and somewhat exhausted. He told me that he had spent his nights and days with adding up digits of divisors of positive ...
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Ernie and the Island of Stability

Unfortunately, it appears that I may have misled you a little in this puzzle (as you probably know - my memory of events isn't always perfect). When I was writing it, I re-checked the Kzijekistanian ...
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Cross-road optimization - what is the proper way to solve this type of puzzle?

This puzzle has 3 levels of increasing complexity. Each "level" is separate and complete, so feel free to post partial solutions to the individual levels only. I'm most interested in the principal ...
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Brothers, cousins, and foes - what am I?

I am one of many siblings in a great family. We are the most perfect of our race, Because each of us has a clear worst enemy. My foe - I know him well - is much like me, But we continually fight ...
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Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
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Should I Take the Bus or Refill My Bottle First?

This is a real-life puzzle encountered by one of my friends. I want to arrive early to my class today. Exactly every $7$ minutes, there is a bus that arrives at the station near my dorm and will ...
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A mathematical riddle

Three letters can define me, Sometimes even just one. Try to derive the answer, And you'll find just me. I'm so fast, I'm so slow, Up or down I will go. Some are based on ...
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Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
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Teacher, teacher on the wall, Who's the dumbest of them all?

A maths teacher writes a very large number on the blackboard and asks her pupils (of whom there are $n$ in the room) about its factors. The first pupil says, "The number is divisible by 2." The ...
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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 ...
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A Cave in the Black Mountains

Across the Deadly River, among the Black Mountains, is a mystical cave. Anyone who enters the cave finds within it a single gold coin, which may be freely taken. Once you leave the cave, you can never ...
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Computation without a computer

In the number $(1+\sqrt{3})^{2015}$, what is the 224th digit after the decimal point? You may NOT use a calculator, computer, or any electronic aid to answer this question. Only pen(cil), paper, and ...
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For Ernie, the task of choosing Christmas presents for his friends is always a struggle. I think that is because, while he finds it easy to solve problems relating to machines, mathematics, and ...
Use the minimum number of ones to make 29. Here is the list of operations permitted: "Standard" operations, such as: $x+y$, $x-y$, $x\times y$, $x\div y$ Negation: $-x$ Exponentiation of two numbers:...
Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...