# 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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### Prisoners and warden game, again?

This riddle is adapted from a certain contest, which will be revealed when the riddle is solved. There are 100 prisoners in a prison. As usual, there is a warden who loves to play games, hence offers ...
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### The Merchant's coin weighing

You're a merchant in the old medieval times, and a customer has come to you to buy something for 13 coins. You know him of course, like everyone in town, and you know he's a sketchy guy. Someone who ...
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### Largest sequence of adjacent numbers less than 11 such that adjacent number divides the other

Friday writes different positive whole numbers that are all less than 11 next to each other in the sand. Robinson Crusoe looks at the sequence and notices with amusement that adjacent numbers are ...
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### Unpaired socks in my lap

Today in my laundry basket I had 10 distinct pairs of socks. I repeatedly take a sock randomly from my basket. If it matches a sock in my lap, I pair both up and put them aside, otherwise I put it on ...
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### Filling a rectangular grid with holes using tetrominoes

There is a rectangular grid of $R$ rows and $C$ columns. $R \times C \bmod 4$ of the cells are painted black, and all other cells are white. In other words, there are at least 0 and at most 3 black ...
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1 vote
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### A 3 digit perfect square and its reverse are both perfect squares. What is the number?

A three-digit perfect square number is such that if its digits are reversed, then the number obtained is also a perfect square. What is the number? For example, if 450 were a perfect square then 054 ...
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### Flip-Flop Firefly Frenzy

Recently, your band of adventurers took on a sketchy merchant who claimed to have a map and password to the Lost Laboratory of Alfonso the Absentminded, an enchanter of great talent and greater ...
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### The Bogotá Marathon

a) Runners at the coming Bogotá Half Marathon have been assigned consecutive numbers starting at 1. Lorena, running for the first time, has noticed that the sum of the numbers of all the athletes with ...
2k views

### What is the maximum number of fish possible in your tank?

You want to put some fish in a square tank. But these fish fight whenever they are in the same tank. Sadly, you have only 1 tank, but you can put glass panes inside the tank to divide it, not ...
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### 3³+4³+5³=6³ Puzzle

A classic puzzle asks us to break a 6x6x6 cube into the smallest number of pieces which can be reassembled into 3 physically separate cubes of sizes 3, 4, & 5. 3³+4³+5³ =27+64+125 =216 =6³ An 8-...
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### Guess the Permutation

Let $p$ be a prime. I chose a secret permutation $a_0,a_1,...,a_{p-1}$ of $0,1,...,p-1$ unknown to you. Now, you can ask the following types of questions to me: Type $1$: Tell me two integers $i,j$ ...
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### The HH vs HT question

My puzzle is based on this tweet (image): Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, ...
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### Today is a prime!

Today, 20240603 already in some parts of the world, is a prime number. Just twenty-one other dates during 2024 are also primes. In what year will there be none?
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### More Catching of Cats

After my first puzzle on this theme was solved relatively quickly, here is a (trickier) follow up question in the same vein! The setup is similar - you are in a room with an infinite line of boxes, ...
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### Making a multiplying magic square

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
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### Long Division when it is almost, but not entirely, wrong

Hmm, my last long division puzzle (Reconstruct a long division given less than a quarter of the digits, and all of those are wrong) didn't last the night. So let's try to make it harder. All of the ...
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### Reconstruct a long division given less than a quarter of the digits, and all of those are wrong

Inspired by "The Puffin Book of Brainteasers" I decided to try my hand at creating a long division missing digits problem where all of the displayed digits are wrong. On searching I found ...
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### Make a Venn diagram with five triangles

A Venn diagram consists of a set of partially overlapping shapes on a plane, arranged in a particular way: for any particular labelling of each of the shapes as "inside" or "outside&...
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### A quantum physics puzzle [closed]

A new mathematical approach to quantum physics via graphs was found recently, see this paper for more details. It particular, it refers to papers by Anton Zeilinger, a Nobel laureate in physics of ...
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### Need some help with my math homework (pretty please?)

Can someone help with a problem from my math textbook? This is the problem I'm stuck on: I don't really get how these kinds of problems work. I think they want me to find the width of the rectangle? ...
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### Catching a Cat on an infinite Line

Upon entering a (very) large room, you are faced with an infinite line of cardboard boxes that are labeled, in order, by the nonnegative integers. In one of these boxes, a cat is hiding, but you do ...
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### Split a number in half, sum it, square it and get the number back

The number 3025 when split in the middle gives us 30 and 25. 30+25= 55. The square of 55 is 3025. What other 4 digits numbers have this property i.e. when the 4 digit number is split in the middle, ...
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### The Ultimate Battle of two players

The Ultimate Battle is a turn-based two-player game. Player $i$ (1 or 2) has three stats: initial hit point $P_i$, attack $A_i$, and heal $H_i$. The values can differ between players. All values are ...
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### Keys and Locks Puzzle

Let $a,b,n$ be positive integers in which $a,b\le n$. You are locked in a room, with $n$ distinguishable keys and $n$ distinguishable locks in it. You know that each lock can be unlocked by a unique ...
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### An elusive hotel guest [duplicate]

From Building Thinking Classrooms in Mathematics: An eccentric woman has booked three adjacent and adjoining hotel rooms. When she checks in, she tells the receptionist that if he needs her, she will ...
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1 vote
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### Solve the Alphametic: SOUNDS / WOW = ELK

This is a long-division problem in which letters are substituted for numbers. Solve the problem. Determine the number value of each letter; and when the letters in each one have been arranged in order ...
375 views

### Can we find four identically colored numbers?

Take the positive integers {1, 2, 3, ...} and color them red, green or blue. Is it true that no matter what coloring is chosen, we can always find three distinct numbers x, y and z so that x, y, z ...
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### Rubik's Cube with no two squares of the same color on any horizontal, vertical or diagonal line

Consider the 12 lines depicted below which all run through the centers of the 9 color squares of a single face of Rubik's Cube. Can you find a scramble such that on each line all squares have ...
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### ORIGAMI: Above and beyond

It's been a long time since I've posted an origami puzzle! An origami puzzle is solved with some thickness $x$ iff it can be folded into a rectangle (possibly a square) with thickness $x$ everywhere. ...
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1 vote
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### find the 3 digits that calculate the same

Suzie was busy working in her office and helping compile Clayton’s expenses for which he has a daily elevenses allowance of less than £10 when she noticed that the three digits making up the amount of ...
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### A "magical" grid progression

Task: fill in the final grid correctly. Hint, if it wasn't obvious enough already:
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### Flipping DIP switches

About 30 years ago, I bought a memory extension card. At first, I was hesitating: there were 8 dip switches and no manual. Then the owner recalled that 4 switches indicated the memory on the ...
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### origami SNY t28

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 28 layers thick everywhere. The purple part is the puzzle. Although solutions are ...
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1 vote
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### A simple cross-number puzzle # 2

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
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### Shortest battleship game, to find the ships

This is a variant of this riddle. A (somewhat peculiar version of the) game of battleship, is played in the following way: The first player places as many ships as he wants on a very large N by N ...
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### Making 1353 using Four fours

As the title says, the goal for this puzzle is making 1353 out of simply 4, 4, 4 and 4. Concatenation is not allowed. Here are all of the allowed operators. Addition (+), Subtraction and negatives (-)...
372 views

### Infinite Towers of Trouble (with a capital T that rhymes with P...)

Friends, we have a towering puzzle in which integers are equated to ordered pairs of colors. The ordered pairs are based on the nine colors given below: White, yellow, blue, red, violet, orange, green,...
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### Visual puzzle involving mathematical operations

Try this puzzle. It involves mathematical operations. Created on my own. CSV (for those who aren't able to see images): ...
1k views

### Shortest battleship game, to find number of battleships

A (very peculiar version of the) game of battleship, is played in the following way: The first player places as many ships as he wants on a very large $N \times N$ board. Every ship is of width $1$, ...
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A positive integer is said to be an Ecuadorian number if for some m, the sum of the first m of its n digits, m < n, is equal to the sum of all its other digits. Numbers such as 11, 134, 235, 2024 ...
422 views

### make seven products equal along sides of heptagon

Inspired by question 126115 Make the three products equal and as large as possible in case someone or 126115 author feels this is plagiarism, be kind and feel free to close Assign natural numbers \$1 ...
1 vote
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### Graph needed which satisfy both properties 1 and 2

We were conducting a tournament where we had 5 teams named- A,B,C,D,E. And in the first round every team played with every other team. So there were 10 matches. But these matches happened during rainy ...
1 vote
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A deadlock is a position in which neither player has won and neither player has a legal placement available. My question is, "Can you find a deadlock position in Minefield?" And, if you ...
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### Two digits in one

Here is a digit: However, it is, at the same time, another digit. How can it be?
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### origami J-SHAPED t2

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The red part is not included in the puzzle; the purple ...
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### Geometry Puzzle: Tangent Circles with Integer Radii

Take as a semi-related example a series of circles with radii 10, 9, 8, ..., 2, 1. Place the first (largest) circle in the center and subsequent circles around it, keeping tangency between subsequent ...
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### Continuing the hexadecimal sequence 9bf66a6a87, 9bfd91c857, 9c0501e2ae, 9c0991af27, 9c0d27e6ec, [closed]

Given the following sequence of hexadecimals, figure out how to generate the next few in the sequence: 9bf66a6a87 9bfd91c857 9c0501e2ae 9c0991af27 9c0d27e6ec My ...
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### ORIGAMI PUZZLES completed version

You may have seen some posts by Sunny Lu here on my origami puzzles. Now, the full version is out! The goal is to fold the paper into a rectangle (or square) with constant thickness (see examples), ...
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