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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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11 votes
2 answers
198 views

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 ...
Culver Kwan's user avatar
  • 5,710
2 votes
0 answers
82 views

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 ...
Ephraim's user avatar
  • 121
1 vote
2 answers
184 views

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 ...
William Bibb's user avatar
12 votes
0 answers
314 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 ...
Will Octagon Gibson's user avatar
5 votes
0 answers
147 views

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 ...
Herbert Kociemba's user avatar
2 votes
1 answer
126 views

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. ...
Sny's user avatar
  • 3,165
1 vote
1 answer
181 views

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 ...
Steve's user avatar
  • 11
7 votes
1 answer
222 views

A "magical" grid progression

Task: fill in the final grid correctly. Hint, if it wasn't obvious enough already:
Auride's user avatar
  • 778
-2 votes
2 answers
210 views

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 ...
kaksi's user avatar
  • 189
3 votes
1 answer
230 views

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 ...
Sny's user avatar
  • 3,165
1 vote
2 answers
332 views

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. ...
Will Octagon Gibson's user avatar
7 votes
2 answers
2k views

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 ...
Rei Henigman's user avatar
8 votes
1 answer
1k views

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 (-)...
Alejandro Garcia's user avatar
3 votes
1 answer
360 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,...
Oscar Lanzi's user avatar
6 votes
0 answers
224 views

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): ...
Fraternal9274's user avatar
10 votes
5 answers
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 $1$, ...
Rei Henigman's user avatar
16 votes
1 answer
895 views

Gaps Between Ecuadorian Numbers

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 ...
Bernardo Recamán Santos's user avatar
3 votes
4 answers
414 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 ...
FirstName LastName's user avatar
-5 votes
0 answers
57 views

Try to make numbers 1 - 100 using 2, 0, 2, 4 [duplicate]

Try to make the numbers 1 - 100 using digits 2, 0, 2, 4 only ONCE. What you're allowed: Basic Operations (+ - * /) Square & Square Roots (Squaring uses a 2) Brackets & Concatenation (e.g. 20-(...
PiMemoryLegend's user avatar
1 vote
2 answers
615 views

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 ...
Durgesh Patel's user avatar
1 vote
0 answers
174 views

Deadlock possible in Minefield?

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 ...
Mark Steere's user avatar
-4 votes
2 answers
370 views

Two digits in one

Here is a digit: However, it is, at the same time, another digit. How can it be?
web adventurer's user avatar
4 votes
2 answers
279 views

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 ...
Sny's user avatar
  • 3,165
7 votes
1 answer
668 views

What does this concatenation operator do?

...
Sny's user avatar
  • 3,165
11 votes
4 answers
595 views

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 ...
Brandan's user avatar
  • 133
1 vote
0 answers
108 views

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 ...
ray's user avatar
  • 11
9 votes
3 answers
533 views

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), ...
Omega_3301's user avatar
8 votes
2 answers
471 views

A simple cross-number puzzle

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. ...
Will Octagon Gibson's user avatar
9 votes
3 answers
1k views

Tiling a 16x16 square with 1x4 rectangles

Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
Will Octagon Gibson's user avatar
14 votes
2 answers
2k views

4,4,2,6,2,10,4,_ sequence from 4th grade packet

The sequence (from my child's "for fun" challenge packet, not for credit or graded) is: 4,4,2,6,2,10,4,_ The possible answers are: A) 15 B) 20 C) 25 D) 28
jmcarson's user avatar
  • 243
6 votes
1 answer
399 views

Next future date such that the all 8 digits of date format DD/MM/YYYY is all different and the product of DD, MM and YYYY is a square number

This puzzle is inspired from here. When is the future date such that the all 8 digits of date format DD/MM/YYYY is all different and the product of DD, MM and YYYY is a square number? Note that "...
Thirdy Yabata's user avatar
9 votes
2 answers
1k views

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9? No two rectangles can be the same size.
Will Octagon Gibson's user avatar
2 votes
0 answers
185 views

Ernie and the conduits of constant cross-section

It all started last week, when Acme Engineering loaned him a prototype version of their 3D Home Printer (this was as a reward for Ernie providing them, patent-free, with a suitable building material - ...
Penguino's user avatar
  • 14k
-3 votes
1 answer
122 views

Apple Sack Reconstruction [closed]

Apple Sack Reconstruction Puzzle Problem Statement: You have an apple tree that can produce apples of four colors: red, yellow, green, and blue. Imagine that you collect all these apples and place ...
Moix's user avatar
  • 5
-4 votes
3 answers
146 views

Use 1 6 7 8 (all numbers) to equal 2 [closed]

Create an equation using 1, 6, 7 and 8 to equal 2. Can use brackets, plus, minus, subtract, multiply.
Number Bond's user avatar
24 votes
8 answers
5k views

Make the number 606 50 percent bigger

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. ...
Will Octagon Gibson's user avatar
11 votes
2 answers
2k views

How can the knight traverse a chessboard to make a path that sums to 100

THE KNIGHT'S CENTURY. THEN Dr. Bates drew on a large sheet of paper a reduced chessboard of twenty-five squares, and numbered it in the manner shown in our diagram. He then placed a chess knight on ...
Will Octagon Gibson's user avatar
1 vote
2 answers
221 views

Diamond Rush: Back to... um

It is summer in the Pse School Of Logicians, and everyone studying there is dying for a break (they absolutely hate school, and can do anything to get out of it). And because the teachers there are ...
3-1-4-One-Five's user avatar
26 votes
5 answers
3k views

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

Can you tile a $25 \times 25$ square (no overlaps, no gaps) with a mixture of $2 \times 2$ squares and $3 \times 3$ squares? This puzzle is by David A. Klarner. Clarification: The number of $2 \times ...
Will Octagon Gibson's user avatar
2 votes
2 answers
379 views

Tournament Scheduling Puzzle

I have an interesting real life problem that can be turned into an interesting puzzle pertaining to a tournament that can be represented in this way: I have 24 people which are assigned numbers 1 to ...
Alex DeCarlo's user avatar
3 votes
1 answer
329 views

Build a slanted pyramid with ten L-shaped blocks

Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Use 10 of the above L-shaped pieces to make the following shape:
Will Octagon Gibson's user avatar
11 votes
4 answers
992 views

Make a square table top with the minimal needed amount of straight cuts

inspired by : Make a square table top with six (or fewer) pieces A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
Retudin's user avatar
  • 9,218
7 votes
1 answer
173 views

A pandigital alphametic

Find, as Ed Pegg did, at least one solution of this pandigital alphametic: A x BC x DEF = GHIJ. How many solutions does it have altogether? (...
Bernardo Recamán Santos's user avatar
5 votes
1 answer
395 views

Dishonest dungeon staff

You are faced with the difficult task to set up a dungeon for adventurers. However you made a deal with the guild: any adventurer brave enough to beat the dungeon and reach the treasure room will be ...
Fluorine's user avatar
  • 1,182
10 votes
2 answers
499 views

Make a square table top with six (or fewer) pieces

A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
Will Octagon Gibson's user avatar
3 votes
5 answers
1k views

Professor Rackbrane: Count the triangles

Professor Rackbrane has just given me the following puzzle as an example of those that interested his party at Christmas. Draw a pentagon, and connect each point with every other point by straight ...
Will Octagon Gibson's user avatar
6 votes
1 answer
233 views

Ernie and the Kzijekistanian Coup

A couple of days ago I noticed an article in the International News section of our local newspaper headlined Kzijekistanian Empress Abdicates. Reading on, I discovered that she "… stepped down ...
Penguino's user avatar
  • 14k
3 votes
1 answer
876 views

How to solve this "Sum things to consider" puzzle? (AARP magazine, April/May 2024)

For context: I am not old enough to be receiving the AARP magazine, however both my parents receive it and I enjoy reading the AARP magazines. I have recently been reading the most recent AARP ...
CrSb0001's user avatar
  • 2,379
10 votes
3 answers
1k views

Fix the addition so that the sum is 1,111

111 333 555 777 + 999 ----- 1,111 The above addition is not correct. Can you fix it? For which numbers $n$ can you change $n$ of the $15$ digits of the ...
Will Octagon Gibson's user avatar
5 votes
1 answer
315 views

Number operation problem - find minimum number of operations

On the blackboard, there are nine numbers from 1 to 9. In each operation, two of the numbers are chosen, erased, and replaced with their sum and difference. If two identical numbers appear on the ...
Vincent's user avatar
  • 53

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