# 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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### Finding the 9 chapters

Suppose that you have a book of 1000 pages. You know the book has 10 chapters and know each chapters has at least 10 pages, i.e., as chapter 1 starts at page 1, chapter 2 can only start at the page 11 ...
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### My Friend's Salary [closed]

My salary is $2,000, I am of Armenian descent and am 31 years old. However my friend, is of German descent and is 26 but he earns$8,000. I think this is blatant discrimination but can you guys find ...
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### Connect Wall With A Fun Fact

Instructions: • Four mystery words are replaced with a double question mark and must be deduced by the solver. NOTE: words are not necessarily in alphabetical order after the mystery words are ...
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### How many uncoordinated cubers does it take to solve a Rubik's cube with multiple solutions?

Inspired by Rubik's cubes with multiple sets of colors or stickers. Suppose there's a Rubik's cube with multiple solutions (represented by multiple sets of colors) made with special paint that reflect ...
3k views

### What’s the highest salary the greedy king can arrange for himself?

A little kingdom contains 66 people, a king and 65 citizens. Each of them, including the king, has a salary of one gold piece. When democracy comes, the king is denied a vote, but he has the power to ...
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### Can you arrange 25 whole numbers (not necessarily all different) so that the sum of any three successive terms is even but the sum of all 25 is odd?

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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### Next date in the future such that all 8 digits of MM/DD/YYYY are all different and the product of MM, DD and YY is equal to YYYY

This problem is a little variation from this problem I made 2 months ago, which is inspired from this post. When is the next date in the future such that all 8 digits of MM/DD/YYYY are all different ...
671 views

### In a circular tray of radius 1, arrange coins of radius 1/2, 1/3, 1/4, 1/5 so that none of them can move independently

In a circular tray of radius $1$, arrange coins of radius $\frac12,\frac13,\frac14,\frac15$ - at least one of each, and no other kind of coin - so that none of them can move independently, i.e. if any ...
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1 vote
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### Strategy for determining graph traversal rules yielding exactly one distinct graph traversal under every permutation [closed]

I am looking for advice/guidance/solutions which can help me with the following problem: Imagine a spatial graph in the x,y-plane arranged in an m x n grid e.g. a 4x4 grid Each vertex in the graph ...
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### Internet Problem Solving Contest 2017 - Problem M

I was practising interesting problems from past problem solving contests when I found this one. I guess that I should find some hash functions to find the candidates and check them by hand. I tried ...
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### Reconstructing Euro results

In the group stage of this year's UEFA European Football Championship, teams compete within six groups of four teams each. Each group plays a round-robin tournament, in which each team plays three ...
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### Find the value of '?' in 4x4 table of numbers [closed]

Solve for ? 50 15 10 60 45 31 5 87 40 22 42 ? 9 4 3 14
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### How can eight quants learn their average salary without revealing individual salaries? [closed]

Here is a problem from section 2.3 (Thinking Out of the Box) section of the popular book by Xinfeg Zhou titled 'Quant salary': Quant Salary Eight quants from different banks are getting together for ...
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### Strategy for solving "Hypatian Enigma" puzzle (all lines add to 38)

The "Hypatian Enigma" puzzle consists of 19 hexagonal blocks numbered 1 through 19. The blocks are arranged in 5 rows. The first and last rows have 3 blocks, the second and fourth row has 4 ...
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### Finding a mystery number - with three logicians

Three perfect logicians named A, B and C each select a positive integer and report their number to Mufti. Mufti writes the sum of the three numbers on one card and the product of the three numbers on ...
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### Find a more elegant explanation for the sequence 01, 10, 13, 20, 25, 30, 37, 40

Some sequences like 1, 2, 4, 5, 10, 11, 22, ... can be explained by a two-part rule: Consider the following sequence: S = 01, 10, 13, 20, 25, 30, 37, 40, ... It is fairly easy to find a two-part rule ...
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### Balls of different weights: how few balls can there be?

This puzzle was inspired by the one in this posting by Hemant Agarwal. There are n balls. Their weights are distinct positive integers which sum to W. The balls have the property that, if any one of ...
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### Finding a mystery number from a sum and product, with a twist

At a party of perfect logicians, Alzim and Era each select a positive integer and and report the number to Mufti. Mufti writes the sum of the two numbers on a card and the product on another card. ...
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1 vote
581 views

### Prove that all 101 balls have the same weight

In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be divided into two groups of 50 balls each with the total ...
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### How fast can you win this (very stupid) game?

You and I get together to play the following (dumb) game: Two positive integers N and K are fixed from the outset. We both start the game with N coins and proceed to play some number of rounds like ...
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### 2,3,6,7 to get 10 [closed]

How do I use the numbers 2,3,6,7 to get 10? You can also make numbers like 23 or 76 too.
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### Prisoners and warden game, again?

Source: There are 100 prisoners in a prison. As usual, there is a warden who loves to play games, hence offers the prisoners a chance to free themselves. He says There is a room with a whiteboard, ...
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### The Merchant's coin weighing [duplicate]

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
247 views

### 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
224 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 ...
466 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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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. ...