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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5
votes
2answers
1k views

Theoretical Puzzle: Making a binary puzzle with a unique solution

If I have a table of binary values, and tell you the column and row counts for "on" or "1" values, is it possible to solve, with certainty, any grid of size n*m? Take the following puzzle for example:...
7
votes
2answers
723 views

A generalization of Tyler Seacrest's “Three voting prisoners” puzzle

The following is a straightforward (but nonetheless not completely trivial) generalization of Tyler Seacrest's great puzzle "Three voting prisoners". There are $n\ge2$ prisoners that have a brief ...
5
votes
2answers
278 views

Checkerboard City versus the ACDWNPP

The Association for the Construction, Development and Wellbeing of Nuclear Power Plants (or simply ACDWNPP for short) plans to build a new nuclear power plant in Checkerboard City. As you all surely ...
6
votes
5answers
2k views

How to maximize your wages?

You're trying to work out how to maximize the wages you receive in the month of February (in a non-leap year). You must work at least 5 days a week and at least 5 hours a day, but you can also work on ...
3
votes
3answers
2k views

Hexagonal sum filling

Q1: Fill this hexagon with numbers 1-19 (no repetition) such that the sum of every vertical and diagonal row is the same. (This should be easy) Q2: Assume that one of these pre-solved cells was not ...
3
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2answers
807 views

Red, yellow and orange numbers

Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are ...
4
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1answer
327 views

The largest Friday number

A Friday number is a prime number N where any three consecutive digits make a prime, and all such primes formed are distinct. For example, 1373 is a Friday number because 137, 373 and 1373 are all ...
6
votes
1answer
176 views

Six days of illness (Part 2)

Professor Doublebrain was severely ill last week, and he had to spend the six days from Monday till Saturday in the hospital. Luckily he has fully recovered by now. He told us that on each of these ...
5
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4answers
1k views

Six days of illness (Part 1)

Professor Halfbrain was severely ill last week, and he had to spend the six days from Monday till Saturday in the hospital. Luckily he has fully recovered by now. He told us that on each of these six ...
4
votes
2answers
462 views

The largest Thursday number

A Thursday number is a number $N$ where any three consecutive digits make a prime, and all such primes formed are distinct. For example, $13739$ is a Thursday number because $137$, $373$ and $739$ ...
6
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4answers
2k views

Cutting from a cube (visualization test)

I had asked this question on Facebook. Imagine a cube. Put it on a flat surface, so that four vertices are at the bottom and four vertices are on top. Select any vertex on top, and connect it to ...
5
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3answers
2k views

The largest Wednesday number

A Wednesday number is a number $N$ where any two consecutive digits make a prime, and all such primes formed are distinct For example, $1371$ is a Wednesday number because $13$, $37$ and $71$ are all ...
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2answers
1k views

What is the minimum number of line segments that need to be made to cross all points on a $n \times m$ grid?

Given a grid of $n \times m$ points, on a sheet of paper, what's the minimum amount of lines (which can extend infinitely) required to pass through each point, that you can draw without lifting a ...
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3answers
400 views

The largest Tuesday number

A Tuesday number is a positive integer $N$ with $d$ digits where the given properties hold true for every positive integer $i$ in the range $0<i<d$ $N\times i$ contains the exact same digits (...
33
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9answers
4k views

Thirty genuine and seventy fake coins

In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions: All genuine coins have the same ...
13
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2answers
1k views

The Erasmus polyhedron

Professor Erasmus has constructed a special convex polyhedron from perfectly homogeneous material, which he modestly calls the "Professor-Erasmus-polyhedron". The professor claims that he can put the ...
28
votes
1answer
3k views

The largest Monday number

A Monday number is a positive integer $N$ with the following three properties: The decimal representation of $N$ does not contain the digit 0 The decimal representation of $N$ does not contain any ...
12
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1answer
594 views

Professor Halfbrain's second cutting theorem

Professor Halfbrain has recently made several fascinating discoveries on cutting convex polygons in the plane. Halfbrain's second cutting theorem: Every convex polygon can be cut (by a perfectly ...
11
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1answer
748 views

Professor Halfbrain's first cutting theorem

Professor Halfbrain has recently made several fascinating discoveries on cutting convex polygons in the plane. Halfbrain's first cutting theorem: Every convex polygon can be cut (by a perfectly ...
2
votes
1answer
158 views

The incredible polyhedron

Based on The Erasmus polyhedron by @Gamow.. Construct a 3D convex polyhedron of any single material that can float in water such that $x\%$ of its volume is below water level and $y\%$ of its ...
0
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1answer
144 views

Curved lines on a paper [closed]

There are curved lines drawn on a piece of paper. Lines can have two characteristics: One of its endpoints is on another characteristic 1 line One of its endpoints is on another characteristic 2 line,...
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votes
1answer
216 views

What number am I thinking of? [closed]

Adding an odd number would make an even number. It's not the largest prime number. But when you divide it into parts I make a multiple of 2. the range never exceeded 100 but never to less from 30. ...
-3
votes
1answer
381 views

Math sequence puzzle

Complete the sequence: 5928 1411 9909 1882 5419 ... It doesn't seem like a simple polynomial fit will work, I have tried the difference method and the quotient method. Any hint would be appreciated. ...
22
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5answers
3k views

Worm and an Apple

Johnny has a perfectly spherical apple, with a diameter of 70 mm. While he looks away, a worm burrows through (entering and leaving) the apple, forming a single tunnel of length 69 mm and negligible ...
10
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3answers
593 views

Find the fastest path through this Brazilian concretist poem

One day, a small jet was flying over the concretist poem "Velocidade" (Speed), by the Brazilian poet Ronaldo Azeredo. In order to cover every vowel present in this poem, it goes in straight line from ...
8
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2answers
772 views

The mini-facebook puzzle

The database of mini-facebook only has space for the data of 100 participants. These 100 participants want to establish as many mini-facebook friendships among them as possible. However, mini-facebook ...
13
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3answers
657 views

Exponential time in a Blue Eyes variant

I created a variant of the Blue Eyes problem where the logic took 4901 days (over 13 years) to totally play out. I thought this was nice, but I was hoping for an even longer period of time. Of ...
2
votes
1answer
180 views

Round plates on a round table [duplicate]

(I did not make this one up, but it's one of my favorites and I didn't see it on here!) After a long shift at the restaurant, your fellow waiter Jeremiah proposes the following game: Start with an ...
16
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8answers
2k views

Rigged casino that prevents pairs

This question is still active as the answer from @Sleafar has just arrived. Not yet solved. Scenario The heads of 3 top terrorist organisations are planning to play an extremely high-stake poker ...
3
votes
3answers
628 views

Line of destruction

There is a line of infinite length (about zero thickness) in a 3D space. It can rotate or move across any plane at any speed. Every point (flagged or not) that has already been visited by the line ...
1
vote
1answer
165 views

Flag carrying ants in a ring [duplicate]

There are $n$ ants randomly distributed on a ring facing clockwise or anticlockwise. Each ant is carrying a flag numbered $1,\ldots,n$. They all start moving around the ring at the same speed (in the ...
5
votes
3answers
556 views

Mr. Hilbert and the Problem of the Nuanced Napkin Ring [closed]

Mr. Hilbert was sitting alone at the dinner table of the Grand Hotel restaurant, waiting for his two friends, Mr. Euler and Mr. Langrange, to show up. It was 5 minutes past six already, but knowing ...
3
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6answers
3k views

Alignment of planets that orbit at different speeds [closed]

If a planet completes its circle around the sun in 120 years and another planet in 70 years then when will they come in a straight line as if they are now?
5
votes
1answer
209 views

Word Matrices, Level 2

This puzzle is based on NeedAName's recent puzzle, Determinant of Word Matrix. The challenge: Create a $3\times3$ matrix of distinct letters (i.e. no repeated letters) with no vowels in the ...
4
votes
1answer
208 views

Literacy in the house

Here is an easy riddle. Recommended for those who haven't studied too much of maths. There are 100 people in a room. $99\%$ of the people in the room are literate. Some people are removed....
9
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3answers
2k views

Jigsaw puzzle: edge and middle pieces

My young daughter and I love doing jigsaw puzzles together. The other day, we had a quite difficult one: 7 by 7 pieces! We started as usual by splitting the pieces into 2 stacks: the edge pieces on ...
-2
votes
2answers
156 views

Walking around in circles [closed]

Imagine you are an ant walking on a circle. You start your journey from the blue point. Your progress is given in percentages - 100% being a full round trip. In the figure, you've made a progress of ...
31
votes
1answer
2k views

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 ...
3
votes
2answers
432 views

Professor Halfbrain's quadrilateral theorem

Professor Halfbrain has recently made a fascinating discovery on quadrilaterals in the plane. Halfbrain's quadrilateral theorem: Let $ABCD$ be a plane quadrilateral that possesses an incircle and ...
6
votes
2answers
517 views

Block the snake from reaching points

Solution for Version 2 pending.... There is a $100\times 100$ grid. The upper left corner has coordinates $(1,1)$ and bottom right corner has $(100,100)$. A 'snake' starts by occupying a single cell ...
25
votes
1answer
1k views

Careless smokers

Cosmo complains: "At the party yesterday at our place, some guys were smoking in our living room. This morning we detected that these careless smokers had burnt four holes into the carpet." Fredo: "...
5
votes
1answer
742 views

Shuffling Cards

I was just thinking about this. Let's say that we have a card deck with 54 cards and the $n$th card from the top is flipped. We repeat a short process of cutting the deck directly in the middle and ...
0
votes
1answer
215 views

Seven Spheres of Unequal Mass, a weighing problem with a twist

You have a scale that is remarkably sturdy, and there are seven spheres of unequal mass. No sphere has the same mass as any other. There is (almost) no limit to the mass of any sphere, but the most ...
12
votes
5answers
424 views

Twitter Followers

There is a group of 300 Twitter users. Each user is following exactly one other user in the group. Prove that there exists a smaller group of 100 users where no one is following anyone else. Source: ...
12
votes
1answer
865 views

Ernie and the Bubbles of Lucretia

"So, what do you know about milking spiders?", asked Ernie as he passed a fresh cup of coffee to me. Good grief!, I thought and gave an involuntary shudder as I glanced at the milk jug sitting ...
0
votes
1answer
205 views

Sum the two numbers

If you know that: TWO + THREE = TILAS THREE + NINE = TUZRI FOUR + TWO = GIRF EIGHT + NINE = EVOUX NINE + NINE = BARAI Can you tell: TWO + NINE = ?
16
votes
1answer
1k views

Hopping from 81 to 82

A grasshopper is hopping around on the integers and starts its journey on the number $81$. In a jump starting from the integer $m$, the grasshopper may jump to any integer $m^k$ with integer $k\ge1$ ...
9
votes
2answers
660 views

$100 + n$ boxes for the king!

There are 100 friends and $n$ enemies in a room. In the next room, there are $100+n$ open boxes, and $100+n$ keys, one corresponding to each box. They are numbered for easy identification. A box can ...
2
votes
3answers
781 views

Don't try this if you don't know your maths!

Find the next number in this sequence: $120, 106, 112, 108, 80, 92, 84,...$ This sequence might be easy for some, but you won't be able to solve it if you don't know a certain subject in maths (...
14
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3answers
1k views

Touching Matchsticks

You are asked to place matchsticks on a flat surface such that each matchstick end meets three others, and no matches cross. It is easy to achieve this for patterns that extend indefintely: The ...

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