# 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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### 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 ...
282 views

### What is a Good Pasta Number™?

This puzzle is inspired by JLee's What is a Word/Phrase™ series and the subsequent "Number" variants. (Actually, I'd originally tried to create a more original puzzle using the same idea, ...
47 views

### 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. ...
93 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 ...
379 views
+50

### 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 ...
439 views

### 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 ...
107 views

### 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.
1k views

### 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, ...
851 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 ...
2k views

### 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 ...
1k views

### 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 ...
132 views

### 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 ...
772 views

### 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? ...
534 views

### 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-...
1 vote
213 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 ...
360 views

### 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 ...
151 views

### 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 ...
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 ...
2k views

### How many times does the earth rotate per year?

Assuming there are exactly 365 days per year, how many rotations about its axis does the earth make in one year?
528 views

### 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, ...
421 views

### 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 $i,j$ ...
1k views

### 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?
37k views

### Find 10 triangles in a five pointed star using two straight lines

This puzzle consists of counting ten triangles (check three sides for each one, remember that there don't exist triangles with more than three sides :P) using two straight lines that cross the figure ...
3k views

### Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes

The first 25 Prime Numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 Using up to 4 prime numbers and the following mathematical operations, get all the 25 primes. + ...
503 views

### Prime to Prime Sequel

This question is inspired by the Prime to Prime puzzle. The first 24 Prime Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 Using up to 4 prime ...
917 views

### Waiting for the gravy at a dinner table

You are sitting at a round dinner table with N other people (i.e. N+1 people all together). One of the other guests is the first to pick up the gravy boat and pour some on their potatoes. It then gets ...
258 views

### 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&...
2k views

### 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 ...
174 views

### 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 ...
25k views

### Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
191 views

### 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! ...
820 views

### 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, ...
220 views

### 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 ...
143 views

### 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 ...
744 views

### Powerful number systems

Imagine I have two positive integers, $a$ and $b$. Can you find the last digit of the sum $a+b$ given only the last digits of $a$ and $b$? More generally, can you find the last $n$ digits of $a+b$ ...
3k views

### 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, ...
1k views

### 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 ...
1k 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 ...
254 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 ...
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 ...
8k views

### Turn the dials until each of the 12 columns add up to 42

I received the wooden puzzle below for Christmas. After playing with it for a while I decided I needed to actually write something down if I was going to solve it. Eventually I just wrote an algorithm ...
92 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 ...
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,...
1 vote
211 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 ...
380 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 ...
137 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. ...
558 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), ...
1 vote
193 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 ...
1 vote
627 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 ...
3k views

### What does this mathematical operator do?

The solution to this puzzle is one I came up with when working on this puzzle: What is the answer of this math puzzle? For two natural numbers a,b, can you figure ...