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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10 votes
1 answer
852 views

A robot that doesn't repeat move triplets

A robot is placed on an empty infinite grid. Each turn it can move in one of four directions: left (L), up (U), right (R) or down (D). It cannot move to a cell that it already visited. Also, it cannot ...
16 votes
1 answer
1k views

What famous meme am I referencing with a polynomial?

What legendary meme am I referencing (twice!) with this large and strange polynomial? $5507x^4-302885x^3+1420806x^2-2224828x+1101400=0$ Buckleyour seatbelts, it’s kind of crazy- I sincerely hope you ...
10 votes
2 answers
1k views

A square number that is a concatenation of at least 25 squares

A pen and paper challenge: Write down a number whose square (repetition allowed) is the concatenation of at least 25 nonzero squares. examples 7, 13, 12: Their squares are the concatenation of 2 ...
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13 votes
4 answers
2k views

Labyrinth of Teleporters

You find yourself in an empty room, with a few distinctly numbered elevated platforms on the floor; your only possession is a pebble that can easily be picked up and placed down. You step on one of ...
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12 votes
3 answers
1k views

Who wins this game?

A 2-player game depends on two positive integers n and k known in advance to both participants. Albert has a secret number from 1 to n. Bob asks Albert a sequence of "yes" or "no" ...
1 vote
1 answer
127 views

Determine the hidden digits in this long division puzzle

The following problem was given in the Eureka journal (October 1963/University of Cambridge). This problem can be solved by hand without computers. There is a unique solution. Have fun solving! Fill ...
3 votes
1 answer
203 views

DD/MM/YYYY and MM/DD/YYYY

A father and his son is from a country where the date format used is DD/MM/YYYY. In 2022, they visited a country for a day where the date format used is MM/DD/YYYY. Predict the birth dates of the son ...
6 votes
4 answers
482 views

Get the treasure from an island of knights and a joker

You've learned that there's treasure buried somewhere on a small island, but not exactly where. The island is a perfect circle with a radius of 25 meters. There are 15 islanders there, one of whom is ...
0 votes
3 answers
193 views

There are 12 parrots in a zoo. 11 parrots out of them have an amazing ability to eat guavas at exactly the same speed [closed]

There are 12 parrots in a zoo. 11 parrots out of them have an amazing ability to eat guavas at exactly the same speed. Just one of them is special and has a different speed of eating guavas. There are ...
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5 votes
1 answer
194 views

Near Magic Squares with the First 25 Primes

There are 25 primes smaller than 100. What is the closest to a 5 x 5 magic square I can construct with them? By "closest" I mean the one with the most columns, rows, and diagonals (12 in all)...
6 votes
2 answers
998 views

What are the hidden digits in this long division puzzle?

The following problem was given in the Eureka journal (April 1978/University of Cambridge). This problem can be solved by hand without computers. There is a unique solution. The phrase, "exact ...
5 votes
2 answers
320 views

'Number couples' dine at Domino's

Different 'number couples' like to dine at Domino's Pizza on the weekends. Different 'number couples' visit at different times (HH:MM format). In case of each 'number couple', HH is the value of one ...
11 votes
1 answer
804 views

---- Add Colours ----

Here is a time waster for you : ) Transcript of the image: ...
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7 votes
1 answer
315 views

Powerful number systems

Imagine I have two positive integers, $a$ and $b$. Can you find the last digit of the sum $a+b$ given only the last digits of $a$ and $b$? More generally, can you find the last $n$ digits of $a+b$ ...
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17 votes
2 answers
918 views

He Hauls Hydra Heads across Hilbert's Hexagonal Hotel

(Special thanks to greenturtle3141 for providing an intriguing narrative backstory to my puzzle.) To aesthetically appeal to his customers, Hilbert has recently redesigned his hotel. You see, all ...
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1 vote
1 answer
120 views

Eggs and family [duplicate]

Martha goes out, carrying some hard boiled eggs in a basket. She meets her sister and gives her half of the eggs in her basket plus half an egg. She meets her cousin and gives her half of the eggs ...
9 votes
2 answers
1k views

How do I solve these Math IQ problems?

This puzzle is part of the Monthly Topic Challenge #2: IQ Puzzle Parody I have no idea how to approach this problem. It is from an IQ test. If you can give me some hints, I will be really thankful. ...
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0 votes
0 answers
185 views

mathematical puzzle whose solution seems to contradict its own hypotheses

This youtube video shows a mathematical puzzle that had me quite baffled, and at the moment I seem to disagree with the solution that is proposed as unique. A leaf is torn from a paperback novel. The ...
-1 votes
2 answers
182 views

What could be a second answer to this direction puzzle? [closed]

What's a second answer? Here's what I have: Pamela's pony is lying exactly north of Becky's bicycle. Alycia's action figure is exactly south of Michelle's stuffed mouse. Pamela's pony is exactly east ...
18 votes
1 answer
4k views

Radical IQ challenge

This puzzle is part of the Monthly Topic Challenge #2: IQ Puzzle Parody Can you find out the next one in the sequence, how it's different to the ones before it, and explain the pattern? 1 10 11 20 31 ...
10 votes
1 answer
946 views

Finish the beautiful, ten story tower

A mathematician has commissioned you to build a beautiful tower, ten stories tall, and it's almost complete! Here are the number of bricks in each level, and the layout of the steel girders. Exactly ...
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2 votes
0 answers
94 views

Three planes fuel tanks for less than halfway around the world - how can one plane make it around the world and what is the minimum fuel tank size?

Inspired by this recent question here is a variation. Three identical aeroplanes are based on an island with one airport. Each plane can take fuel to get less than halfway around the world. Fuel can ...
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7 votes
3 answers
380 views

Avoiding arithmetic progressions in square grids

a) Is it possible to place the integers 1 to 25 in a 5 x 5 grid so that no column or row contains an increasing or decreasing 3-term arithmetic progression (A.P.)? b) Can this be done in a 6 x 6 grid ...
18 votes
6 answers
7k views

Three airplanes with enough fuel for halfway around the world - how can one make it all the way?

Consider three identical airplanes starting at the same airport. Each plane has a fuel tank that holds just enough fuel to allow the plane to travel half the distance around the world. These airplanes ...
  • 603
5 votes
0 answers
229 views

What is a Good Pasta Number™?

This puzzle is inspired by JLee's What is a Word/Phrase™ series and the subsequent "Number" variants. (Actually, I'd originally tried to create a more original puzzle using the same idea, ...
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11 votes
2 answers
3k views

Sharing 41 sticks among 42 people

Question: Ali-Baba is a prisoner of the $42$ thieves who have just stolen $41$ identical magic incense sticks. The thieves want share this loot in such a way that everyone has exactly the same pieces ...
  • 113
7 votes
2 answers
924 views

The Road to a Fulfilling Life

The final answer is a 12-letter word and is confirmed by the title. Other applicable tags: visual, enigmatic puzzle, rebus (stage 2) Stage 1 of 2: Mark the correct cells black in the 5 grids below and ...
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6 votes
1 answer
415 views

Find all integers n such that $\sqrt{n-4 \sqrt{n-19}}$ is also an integer

The following puzzle is from the December 2012 issue of the Eureka journal (published by The Cambridge University Mathematical Society). Find all integers n such that $\sqrt{n-4 \sqrt{n-19}}$ is also ...
8 votes
2 answers
492 views

Two cornucopias and infinitely many gold coins

There're two cornucopias of infinite volume, each with one gold coin in them. Right now $t=0$. A new coin will be born at $t=\frac{2^n-1}{2^n}$ for every positive integer $n$. Each new born coin will ...
  • 5,187
0 votes
2 answers
139 views

How can 8 , 10 or 12 teams rotate through 7 or 8 games without overlaps? [closed]

We are scheduling a big scout event with children, and we have 7 or 8 games organized for them to rotate and play with each other. Set up a game schedule that follows these rules: There are 3 ...
1 vote
1 answer
118 views

Diversified Rubik's Cube [duplicate]

I have, cleverly I hope, shuffled my Rubik's Cube for a while. I could not find a position where, for each faces, all colors appear 3 times or less. I always had a or several faces with at least 4 of ...
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0 votes
1 answer
153 views

Puzzle regarding 100 random objects of different sizes, and choosing one at random one at a time to get largest

Basically, the riddle at hand was used to demonstrate a principle (of which I forgot), and it was asked thusly; I know there are other forms of it, but here goes: You are fishing in a pond of 100 fish ...
  • 3
12 votes
1 answer
2k views

The Lufthansa Lottery

In order to pass free time while striking for better pay, some Lufthansa workers organise a lottery where each ticket picks three distinct numbers from $1$ to $11$ inclusive the draw picks five ...
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28 votes
1 answer
2k views

What's the most important life lesson?

Important Life Lessons: Life can be a confusing game at times. Here's some important lessons you should follow: Time stops for no man - Life is always changing, before you know it, there could be ...
7 votes
1 answer
913 views

The jealous engineer problem

One day Tony woke up and didn't find his wife in the house. — Where were you? — I wanted to work out and just walked around the block. Look at my pedometer. — What distance does the pedometer show? — ...
0 votes
1 answer
152 views

Number of 6-person events so all groups of 3/10 people have dined together [closed]

Assume 10 people numbered 1-10 have to be invited for dinner events. However, the hotel can accommodate only 6 at a time. Therefore, they will be invited in batches until all groups of 3 people have ...
  • 103
6 votes
3 answers
1k views

Double chess stalemate with 60 units

Inspired by Symmetrical Chess Position With No Legal Moves Can you arrange on a chessboard 18 kings, 6 rooks and 6 bishops of each colour (i.e. 60 units, leaving 4 empty squares) so that neither side ...
  • 1,197
-1 votes
1 answer
81 views

String bit pattern puzzle [closed]

For the purposes of this puzzle, a "string" means a sequences of zeros and ones, e.g. 1011. Consider all the different strings of length eight — a good first step would be to figure out how ...
  • 603
6 votes
1 answer
294 views

36 * 8 = 44, 27 * 12 = 23

Was playing a game today and encountered this puzzle. What's the rule behind it? 36 * 8 = 44, 27 * 12 = 23 19 * 4 = 43. Therefore, what is 50 * 8? The answer is Source: Black desert online, the ...
  • 163
9 votes
0 answers
522 views

Gold and silver coins in sealed envelopes

Alice has freely chosen to put either a gold coin or a silver coin in each of an infinite sequence of envelopes numbered 1,2,3,... Bob can open any number of envelopes and check the coins within, ...
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23 votes
3 answers
2k views

A pentagon that can measure the first 7 integer distances

A pentagon can be used to measure 10 distances - one distance between each pair of its 5 vertices. Can you find a pentagon that can measure every integer distance from 1 to 7, inclusive?
8 votes
1 answer
379 views

Who owns The Golden Pie Café?

It's the early second millennium, and we're in Italy's two-dimensional cartesian world, and look, Mr.X has just opened a new café—The Golden Pie Café! He's put a lot of thought into constructing the ...
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2 votes
2 answers
703 views

Cut a square piece of paper

You are given a square piece of paper shown below: Can you cut this paper in a way that: The shortest distance from A to B is double the shortest distance from A to C; and The shortest distance from ...
8 votes
2 answers
1k views

Number of divisors equals square root

A colleague of mine mentioned that there was something special about the number nine. He noticed that nine had three positive integer divisors {1, 3, 9} and the square root of nine is three. His ...
5 votes
1 answer
268 views

Function that is 0 for all positive integers divisible by x and 1 otherwise

I am working on dice probabilities and I need a function where every xth item of the set of positive integers > 0 (n) is 0 and 1 otherwise.* x is also a positive integers. So, can you, without the ...
  • 161
18 votes
7 answers
6k views

Make 2 0 2 2 2 0 2 2 = 2022 [closed]

Inspired by this puzzle, I've come up with the following: Can you find a way to make $2 \; 0 \; 2 \; 2 \; 2 \; 0 \; 2 \; 2 = 2022$ by only adding any of the following operations or symbols: $+,\ -,\...
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4 votes
1 answer
197 views

Are there Stars on the Knight Sky?

If you watched the Queen's Gambit you'll know that there are lots of upside-down chess boards all over the world's ceilings. If not just take my word for it. The same is true of the actual sky only ...
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2 votes
1 answer
107 views

What is the name of this problem about maximizing the accepted offer from consecutive offers?

There was a problem I have read more than 15 years ago. I just remember the problem and the rough outline of the solution, and I would like to know if it has a canonical name to look up the ...
3 votes
3 answers
576 views

rope - knotted or does not knot [closed]

The figure shows the shadow of a piece of rope on the ground, and you can't see which part is on which part; Suppose the rope is placed completely randomly. Now tighten the two ends of the rope to the ...
  • 101
5 votes
2 answers
214 views

Robot painting a $K_5$

A robot starts at a node of a fully connected graph of 5 nodes (shown below). Each turn the robot can move across an edge and paint it in one of two colours - blue for odd turns and red for even turns....

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