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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2 votes
1 answer
128 views

Harary's generalized Tic-Tac-Toe; Winning strategy for Skinny on a 7 x 7 board?

Disclaimer: The purpose of this post is a ask question, not to offer a puzzle. Still, there are some puzzles here for the reader's pleasure. Disclaimer 2: This question was also asked on Math Stack ...
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3 votes
1 answer
203 views

Shuffling blocks puzzle

We have 5 blocks denoted A, B, C, D, and E. Let's stack them in two layers such that block A and B are on the top and blocks C, D, and E are on the bottom. Call this arrangement ABCDE: Let there be ...
5 votes
2 answers
230 views

How many coins did Raj get?

I found a bunch of coins: Quarters (25 cents), Dimes(10 cents) and Nickels(5 cents). The combined amount was a whole two digit number of dollars: that is, no fractional amount. I divided the coins ...
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4 votes
1 answer
656 views

When is my birthday?

Who am I? When is my birthday?
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27 votes
3 answers
3k views

How many fingers do the inhabitants of this planet have?

Actual Puzzle After crash-landing your spaceship on an uncharted planet, you run across the following drawing: $\begin{matrix} ⊙ & × & × & ⊓ & ⊓ & ⊙ & & \\ ⊙ & ∿ &...
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2 votes
1 answer
246 views

Prove the existence of a triangle such that all of its sides are of the same color [closed]

Seventeen points have been picked in a plane, and each pair of points has been connected by a line segment of one of three colors: red, yellow, or green. Prove that there are three points which are ...
2 votes
1 answer
167 views

Five 3:1 rectangles tiling a square

Can you fully tile a square with 5 rectangles such that: Every rectangle has 3:1 ratio, ie., their length is triple their width. No part of any rectangle is outside the square. No two rectangles ...
2 votes
2 answers
221 views

Quickest chess stalemate with Queens exchange

Continuing my previous puzzle. If both players cooperate, what is the quickest stalemate in chess that includes a Queens exchange, in a legal game?
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4 votes
2 answers
363 views

Seven 2:1 rectangles covering a square

Can you fully cover a square with 7 rectangles such that: Every rectangle has 2:1 ratio, ie., length double its width. No part of any rectangle is outside the square. No two rectangles overlap. Note ...
-4 votes
3 answers
140 views

What is the Result of this icon Equation? [closed]

from:https://www.rondogo.sk/hra I have problem with heart :) A) 19 B) 20 C) 21 D) 22
4 votes
3 answers
969 views

Finding a Kakuro trick

The following screenshot is taken from the Android app Kakuro++ (level 9 riddle 12) And I verified the current status within the app. I managed to solve the puzzle by guessing a 50/50-number and ...
0 votes
1 answer
220 views

My wish that I can't see

There's fire outside. The world is collapsing, it's over. It's not going to be just fine; it's never going to be. I sing nothing. This is not of mine. $\sin\theta \sec\theta$ is all I have, even ...
4 votes
1 answer
392 views

SECRET PUZZLER EYES ONLY

Today is my 40th birthday and I will be celebrating by sharing a puzzle with you all. I recently stumbled upon an abstruse image, and apparently the words in main body of the image all have something ...
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3 votes
1 answer
257 views

The two numbers which were overestimated

James: These two cards have two numbers $X$ and $Y$, which are both one-digit numbers and are different. Can you find the sum? Jack: No, that's impossible. Can I get a hint? James: The last digit of $...
2 votes
1 answer
278 views

What number is missing in the pentagon? [closed]

What number is missing in the pentagon? Puzzle from: https://www.rondogo.sk/hra/
5 votes
1 answer
192 views

Fill in the blanks with numbers

A simpler version of this puzzle was by @Sid on PSE Fill in the blanks with the number in words Here is a bit challenging version Fill in the blanks with numbers (in words) for the following: This ...
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8 votes
4 answers
889 views

Splitting integers and taking differences, how can the sum be constant?

Start with the set of integers from $1$ up to $2n$, where $n$ is a natural number. Split this set into two disjoint subsets of equal size, say $\{a_1<a_2<\cdots<a_n\}$ and $\{b_1>b_2>\...
2 votes
1 answer
335 views

Thirteen Diagonals of a Nonagon

A regular nonagon has 27 diagonals, and these diagonals intersect in the interior of the nonagon at 126 distinct points. Show that it is possible to select 13 diagonals of a regular nonagon such that ...
5 votes
1 answer
206 views

Insert Plus Signs and Add

If you take any integer (in base 10) and insert plus signs, "+", in between its digits (as few or as many as you like), and carry out the indicated sum, you will end up with a smaller number ...
25 votes
2 answers
2k views

An easy trillionth power

Hardy was revisiting Ramanujan and this time arrived in taxicab number 1792. He remarked that this number seemed rather dull. Ramanujan replied, "It is very interesting, it is the product of the ...
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4 votes
1 answer
399 views

a paid day/cOmes, goEs away quIck, So/much became/of a juco

The entirety of this puzzle is contained within the title. Your final answer should be a single word.
0 votes
2 answers
380 views

A certain 'Monty Hall' variant was played. How many doors were there, and, what was the value of the prize?

Recall the standard Monty Hall scenario where a presenter hides one prize with high value $h$ behind one closed door (e.g., in the classical version: the one high prize is a car), and, equal prizes ...
2 votes
1 answer
192 views

How useful is Marijn's Bluff?

Parcly and Tori Taxel, after having wished genies' chess into existence and played around with it – noticing the link to Zarankiewicz's problem and getting an OEIS entry published in the process – ...
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6 votes
2 answers
304 views

Jigsaw puzzle: packing pentominoes into a rectangle

I've got this jigsaw puzzle that I can't figure out. The major problem is that there are no signposts on whether a piece is in the right place. How does one get all the pieces into the 6x10 container? ...
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1 vote
1 answer
100 views

Equal row-products and column-products in a given array [closed]

I don't know if this is the right place to ask this question, but I'm stuck on this and can't figure out how to even proceed. Any hints anyone? Is it possible in a 5 × 5 array of integers for all row ...
3 votes
1 answer
413 views

Genies' chess on a 10×10 board

The work of Hearth Taxel revealed some other results related to genies' chess. For example, there is an arrangement $A$ of pawns on a 10×10 board such that no 3×3 submatrix is empty and $A$ is ...
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2 votes
2 answers
386 views

Two genies and their kind of chess

While playing chess Parcly and Tori Taxel, best friends and genies, got bored and transformed all the pieces into pawns to make pretty patterns. They found this 22-pawn arrangement where every 3×3 ...
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0 votes
1 answer
145 views

A Complex Dash To Stalemate

For today's contribution to PSE, I present a sliding block puzzle! I have a series-helpstalemate in 26 for you all with a relevant question attached. The illegal position is intentional. Objective #1: ...
2 votes
1 answer
232 views

A puzzle in tribute to J. J. Sylvester

About the right time of the year I say, since Sylvester's Day is nigh. AFAIK the puzzle is original; comments welcome if you know any better. (Edited) Sylvester's theorem, also Sylvester-Gallai ...
15 votes
6 answers
3k views

Three horse race

There are three horses in the race. You know the following information about them: Horse A will finish the race in 50 or 60 seconds with both events being equally likely. Horse B will always finish ...
12 votes
1 answer
1k views

A hidden number everyone is talking about

The following describes an 8-digit positive integer. Identify this number, and explain the title of this puzzle. The number is in the form of 2021____. It has 24 ...
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8 votes
3 answers
237 views

Place digits from 1 to 7 into each row and each column of the grid once. Numbers in the circles give the product of the four surrounding digits

What is the way to resolve the following puzzle? Link to source. It's from a taiwanese math olympiad held in 2005.
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26 votes
1 answer
2k views

What is a Chess Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a Chess Number™. Use the following examples ...
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5 votes
1 answer
283 views

Connecting points to form triangles

$3n$ points are drawn on a flat piece of paper, such that no $3$ points lie on a straight line. Is it always possible to connect triples of points with straight lines, such that you form $n$ triangles ...
8 votes
2 answers
388 views

12 coins problem but you can't understand the scale

You have 12 coins 11 are real, one is fake but you don't know if it is lighter or heavier. You have a scale that gives you output but you don't understand it (let's say it is written in a foreign ...
8 votes
1 answer
214 views

Ernie and the Christmas Stars

Although Ernie professes to be an atheistic rationalist, he does love the Christmas season. He thinks long and hard to find appropriate gifts, brushes up on his Christmas Carol repertoire, plans a ...
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7 votes
2 answers
1k views

A rectangle cut into two pieces, which build a square

A rectangle with side length a and b are in ratio $a : b = (n+1)^2 : n^2$, where n is a positive integer. Is it possible to cut each such rectangle into two pieces, which can be put together to build ...
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7 votes
3 answers
2k views

Help needed with my niece's math puzzle

My niece is having problems with the attached and I can't figure it out. I think I'm overcomplicating it. Does anyone have thoughts on how to solve it?
10 votes
0 answers
155 views

Rigid regular nonagon from 21 Meccano strips

You are given 21 Meccano strips, where the distance between adjacent holes is 1 unit: 9 strips of length 10 (hence having 11 holes) 6 strips of length 18 (19 holes) 6 strips of length 19 (20 holes) ...
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1 vote
1 answer
195 views

How can the princess escape the prince?

This is the story of the sister of the princess in this puzzle. I will shamelessly copy-paste some parts of this post. I have no reference to give for this version as I adapted a Computer Science ...
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0 votes
2 answers
147 views

How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day

My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team. I have 150 open slots every day (5 days a week) for those 20 teams ...
2 votes
3 answers
260 views

Reversible number problem

These are the reversible numbers In this example we have an operation that on one side gives the result 6 and turning it gives it 12. Is it possible using reversible numbers and mathematical ...
4 votes
2 answers
550 views

How many seats around the table?

This puzzle is very much inspired by a recent, excellent, one, posted here. If anyone, in particular the author of the other puzzle, prefers this one to disappear, I will immediately do so and I ...
2 votes
1 answer
148 views

Find two integers based on their sum and a random number

Alice, Bob and Charlie play a game. Alice writes down two positive integers on a blackboard visible to Bob and Charlie. She says that one of them is of her own choice, the other number is the sum of ...
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8 votes
2 answers
490 views

Form an equilateral triangle

Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $4$ points. They're free to mark their points anywhere ...
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5 votes
4 answers
444 views

Algorithm to make two scrambled Rubik's cubes be exactly the same on all faces

There are millions of Rubik's cube combinations possible. If I have two 3×3 Rubik's cubes and both are scrambled, I want to make one scrambled cube exactly the same as the other without solving them. ...
13 votes
1 answer
492 views

Enigmatic maths

$\left\lceil{\left(\left(2-1\right)^{19}+5\right)^{\left(\frac{20-23-5+14}{\left(\cos\left(\cos\left(\sin\left(\sqrt{\ln\left(\ln\left(\frac{20-\sqrt{25}\cdot19}{9-24}\right)\right)}\right)\right)\...
3 votes
1 answer
340 views

How many consecutive integers to ensure one has digit sum divisible by 19?

How many consecutive positive integers are at least required, such that there is always a number in such a sequence whose sum of digits is divisible by 19?
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3 votes
1 answer
117 views

Two pairs of dice with the same probability [duplicate]

Alice has two dice each numbered from 1 to 6. Bob has two dice as well, the numbering is not known, but each face has a positive integer. The numbering on each dice can be different and a number can ...
  • 11.6k
12 votes
2 answers
704 views

Introducing S-sequences: which is the shortest to contain all integers 1 to 20?

Consider a sequence (finite or infinite) of different positive integers, such as the following, in which the first term is 1, and thereafter the nth term is either the previous term plus n, minus n, ...

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