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.

Filter by
Sorted by
Tagged with
9 votes
4 answers
2k views

Haselbauer-Dickheiser Test no. 3: Circle divided by lines between a blue dots

This is the test no. 3 from Haselbauer-Dickheiser Test. 3. These three circles below all have blue dots on their circumference which are connected by straight lines. These lines divide the ...
14 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 ...
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" ...
8 votes
1 answer
401 views

Origin of the "Ages of Three Children" puzzle (Census-taker problem)

There is this puzzle and many variations of it, but it usually comes by as "Ages of Three Children puzzle" (Wikipedia article), the "Census puzzle" (mathsisfun.com, YouTube video), ...
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 ...
10 votes
1 answer
943 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 ...
3 votes
2 answers
218 views

Cube the digits and carry on

Take a number between 2001 and 2100 inclusive. Cube the digits of the number and add them together, then repeat the process with the new sum and restart the process over and over. For example if I ...
3 votes
2 answers
272 views

Magic: The Gathering – projecting images

You are in a Magic: The Gathering commander game. It is now your first main phase and you control these permanents: One Miirym, Sentinel Wyrm: "Whenever another nontoken Dragon enters the ...
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
278 views

Four color a map - but go light on the fourth color!

Here's a map, which I found here: Your challenge is to four-color this map while minimizing your use of the fourth color. More specifically, color the map with four colors so each region is a ...
110 votes
3 answers
10k views

Prove that π > 3

It seems that once upon a time some politicians tried to pass a law fixing the value of π to be exactly 3. The idea being to "make math simpler so that our children can get better at math". ...
1 vote
1 answer
121 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
198 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
477 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 ...
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 ...
34 votes
3 answers
1k views

Translating a fiendishly exceptional automorphism of $S_6$ into a lay-math puzzle

Foreward: This post not a puzzle in itself, but an invitation for you to show off your puzzle-making skill regarding a given topic. Although the tag description of "puzzle-creation" seems to ...
5 votes
1 answer
193 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)...
0 votes
3 answers
190 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 ...
7 votes
1 answer
314 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 $a+b$ ...
14 votes
4 answers
1k views

The mower's challenge

Weeds have taken over the roads. If mowed, they don't grow back, but unmowed weeds spread at speed 1 along the road. What's the minimum speed of the mower to get rid of all weeds? Roads are connected ...
0 votes
1 answer
237 views

What is this card matching game/trick?

As a kid I used to do this card game/trick a lot but I can’t remember what it is or how to do it anymore. All I remember is that it used math or counting. You had a certain amount of cards sort of ...
6 votes
2 answers
995 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
801 views

---- Add Colours ----

Here is a time waster for you : ) Transcript of the image: ...
17 votes
2 answers
913 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 ...
7 votes
3 answers
1k views

How many digits can be removed from a division puzzle?

Similarly to How many digits can be removed from a multiplication puzzle and still give only one answer? I am curious about division puzzles. I know this puzzle: . It has only 2 out of 42 digits $\...
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. ...
12 votes
6 answers
5k views

20 cards facing down

You have a row of $20$ cards facing down. A 'move' consists of the following actions performed in sequence: Pick a face-down card and flip it face-up If there is one, also flip the next card on ...
0 votes
0 answers
184 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 ...
23 votes
3 answers
1k views

An ant's walk in the Cartesian Plane

An ant lives in the origin of the Cartesian Plane. Every morning, at 6 am, it sets out on a 16-hour walk which gets her back home precisely at 10 pm. In the first hour the ant walks exactly one unit, ...
-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 ...
32 votes
4 answers
3k views

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 ...
7 votes
3 answers
378 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 ...
19 votes
8 answers
4k views

Logical puzzle from a math homework for Russian fifth-year school students

The daughter of a relative of mine, a fifth-year school student in Russia, got the following math homework from her teacher: Here's my translation: Logical task No. 26. Students were solving a task ...
6 votes
1 answer
411 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 ...
2 votes
0 answers
93 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 ...
8 votes
2 answers
490 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 ...
0 votes
1 answer
154 views

Generalization of twelve balls and scale problem

This problem is a generalization of Twelve balls and a scale problem. So I can solve and understand how things are going if we have 12 balls or 9 balls but how do I generalize? If say we have $3^n$ ...
8 votes
3 answers
397 views

The children of the sultan

An old challenge from an old Portuguese book I have: Abdul Al-Kwaritz-Amuhmahd was a Arabic sultan who became very famous by the size of his harem and the number of children he had fathered. More so ...
73 votes
20 answers
29k views

Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
5 votes
0 answers
228 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, ...
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 ...
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 ...
5 votes
1 answer
266 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 ...
0 votes
2 answers
138 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 ...
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 ...
1 vote
1 answer
117 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 ...

1
2 3 4 5
85