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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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6 votes
4 answers
411 views

### Approximate ln(2) out of small numbers

Given numbers 1,2,...n, the goal of this puzzle is to make a number as close to the mathematical constant $\ln(2) ≈ 0.69314718055$ as possible. Rules You can only use the four mathematical ...
• 2,423
17 votes
2 answers
2k views

### Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard. Bob appends another digit from the set M until a 2n-digit ...
• 12.2k
7 votes
1 answer
339 views

### Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
• 1,261
3 votes
3 answers
265 views

### All poker hands from a single deck

This question suggested itself to me – and I found a solution – after I solved Can you balance this poker deck?. Take out two aces from the standard 52-card deck. Your challenge is to partition the ...
• 7,820
4 votes
1 answer
274 views

### Can you balance this poker deck?

You are given the digits 0 to 9 in 4 poker suits. Distribute them onto the 8 highest poker hands (make one of each) of 5 digits each. They are Royal Flush (9 to 5 of one suit) Straight Flush (...
• 389
13 votes
7 answers
2k views

### Fewest number of prisoners needed

You are an assistant to the king, who has scheduled a party tomorrow. There are 1000 wine bottles in the king's possession, and unfortunately, 3 of them are poisonous. Consuming from any of these ...
12 votes
1 answer
950 views

### Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
• 12.1k
9 votes
2 answers
295 views

### How do I constrain a puzzle and keep a singular solution?

I am tinkering with a puzzle framework that has the following rules: In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
• 143
24 votes
2 answers
1k views

### Hexominos from pentominos, heptominos from hexominos

All twelve pentominoes can be obtained by attaching a single unit square (edge to edge) to one of the squares that make up one (or more) of the following four tetrominoes: a) What is the least number ...
-2 votes
1 answer
109 views

### How to make all the numbers ranging from 1-30 only using the numbers 1, 5, 0, 4 [closed]

You can use the numbers 1, 5, 0, and 4 but you can't square and cube, you can't use any other numbers, you can't use the numbers more than once, your answer can't be rounded, and you MUST use all the ...
4 votes
1 answer
175 views

### Curious statements about black cells on a grid

Consider a finite rectangular grid consisting of unit squares (cells). Some cells are colored black, and the rest are white. Some definitions: Two black cells are neighbors if they share an edge. Two ...
• 15.6k
24 votes
2 answers
4k views

### A pizza dilemma

You are a waiter at a restaurant. The restaurant is known for its signature dish: the Donut Pizza. The Donut Pizza is a 5-inch square pizza with a 1-inch square hole in the middle. After several ...
• 1,261
2 votes
1 answer
147 views

• 2,423
3 votes
1 answer
372 views

### Place numbers 1 through 9 in boxes (☐☐×☐=☐☐+☐☐=☐☐)

So recently I was scrolling through Youtube when I came across this video from MindYourDecisions that was about solving a legendary math puzzle. The puzzle: Place the numbers 1 through 9 in the ...
• 2,423
2 votes
4 answers
483 views

### Divide rubies and diamonds on a necklace into 2 equal halves

Two thieves steal a necklace consisting of 10 rubies and 14 diamonds, fixed in some arbitrary order on a loop of string. Show that they can cut the necklace in two places so that when each thief takes ...
• 3,157
8 votes
2 answers
423 views

### The shady puzzle that will keep you in the dark

The image below is the horizontal cross section of a room. The bulb shows the position of the single light source. When the light is switched on, one wall (marked in brown) remains completely in ...
• 12.1k
19 votes
1 answer
1k views

### An Amazing Configuration

Ed Pegg found in December 2019 this amazing configuration consisting of 22 points in 28 lines of 4. On those points place 22 different positive integers such that the sum of any of the four points in ...
38 votes
4 answers
3k views

### Pythagorean pentagons

To follow up on the theme of so called "pythagorean" dissections, here is one more for you to chew on. I hope you don't get bored. The pentagons above have sides respectively 3, 4 and 5. ...
• 30.6k
1 vote
1 answer
202 views

• 438
-3 votes
1 answer
222 views

### What day of the week I am?

I am the day of the week that wants to be the first day of a year that is a perfect power. I do not like odd years. In order to be a perfect power, the year must end one day of the week later than the ...
7 votes
1 answer
503 views

### Productive Squares

Consider a productive square of size $n$ to be an $n\times n$ grid filled with a permutation of the integers in $[1, n^2]$, such that the product of all the numbers along the first row is equal to ...
• 3,185
-2 votes
1 answer
173 views

### Maths olympiad of class 10 [closed]

How many 6digit numbers of the form XYZZYX (where Y is prime) are possible which are divisible by 7 A 42 B 56 C 70 D 84
0 votes
2 answers
160 views

### Seven birds in search of food [closed]

Seven birds live in a nest. They are very organized; each day three of the birds fly out in search of food. In n consecutive days, every pair of birds has been in exactly one of the n daily search ...
4 votes
2 answers
207 views

### Strings of Kind Numbers

A positive integer is said to be “kind" if it is divisible by one of its digits other than 1 (https://oeis.org/A185186). A kind string of numbers is a finite sequence of numbers all of whose ...
5 votes
2 answers
355 views

### Making an expression with the numbers 1 to 100 odd (or even)

Anna and Boris play a game with the numbers from 1 to 100 written in order in a row. Anna goes first, and turns alternate thereafter. In each move, a player puts one of the operation signs +, − and × ...
• 12.1k
8 votes
3 answers
1k views

### Walking in a random direction

I walk $\pi$ km in one direction followed by $\pi$ km in another direction. In expectation how far am I now from my starting location? Both directions are chosen uniformly at random between $0^{\circ}$...
• 36.2k
0 votes
1 answer
390 views

### Rooks covering Dark Squares on a Chessboard

How many rooks are required such that all dark squares on the chessboard are covered by at least one rook.
• 3,185
1 vote
0 answers
60 views

### Change all eight numbers to 1 [duplicate]

A solitaire game starts with eight numbers arranged in a circle. Each is either 1 or −1, and the choice is arbitrary. In each move, one can multiply any three adjacent numbers by −1. Prove that one ...
• 12.1k