# 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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### Nondivisibility by 11 puzzle

Source: MacPOW Problem of the Week 1240 Take this math puzzle: The number 545 has the curious property that upon replacing the digit in any single position by an arbitrary digit (from 0 to 9; it can ...
571 views

### How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

I consider it an amazing though very challenging puzzle: 1 2 3 4 5 = 5 4 3 2 1 One must insert exactly five pluses (i.e. five addition signs) somewhere between those ten displayed figures in such way ...
313 views

### Zeroes in natural numbers up to a googol

How many times does the digit $0$ occur in the list of numbers from $1$ to $10^{100}$, inclusive?
3k views

### Which parent should you start playing against?

Let $k < n$, $k$ even, $n$ odd. Mary is to play $n$ chess games against her parents, alternating between her father and mother. To receive her allowance she must win $k$ games in a row. Given the ...
123 views

### Obtain all digits using only 0

Combine digits you have into numbers and perform mathematical operations with them to get the rest of the digits. You may use all mathematical operations. You start with 0. Example: You have digits 0,...
867 views

### A Sierpiński Carpet ratio

This math problem popped into my head and I wanted to share it with you: We have the Sierpiński carpet, which is a fractal built like this: Draw a square. Divide it into 9 equal subsquares arranged ...
2k views

### Let's break PolynumCrypt

Introducing a super secure function to crypt your sensitive data - PolynumCrypt! Say you wanted to crypt the string $\text{super}$, with a key of $6$. Get the ASCII values of the string, ...
575 views

### How to sell at the buying price and still have something in hand? [closed]

A farmer walked into the cattle market and found the price is fixed at "5 for 2 coins", either buy or sell. He thought a little and then bought cattle of 250 cows for 100 coins (250/5 * 2). ...
3k views

### Two-Move Chess Game

Consider a standard game of chess. We make the following modification: on a turn, if a player makes a move which neither captures a piece nor puts their opponent’s king in check, then they may make a ...
466 views

### $\pi$ = 13, $\sqrt{2}$ = 7, $e$ =?

From The Escape Room Advent Calendar: Puzzle book for adults I know the answer to this puzzle. I cannot for the life of me figure out why it is what it is.
381 views

### Irregularly Deposited Compound Interest

Suppose you have a very peculiar bank account that obeys the following rules: The account pays 10% interest per year, generated continuously. Interest from the account does not compound automatically;...
253 views

### Nimber mnemonic combinatorial puzzle

Please see my previous question for more background. The following represents an unfolded version of PG(3,2) with 1 as the center point: Given that each number must be an end point of a line which ...
3k views

### Mishustin's circle problem

This problem was given to high school students by the Russian prime minister Mishustin. We have a circle. We are given some point on the circle and its diameter, as shown below. We are given a ...
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### Minimum function optimization puzzle #4: Using negative numbers?

Previous puzzle Take this puzzle of mine that I created around a week ago: Take these 3 functions: $f(x):=x+8,g(x):=x^2-3,h(x):=\sqrt x$ Starting from $x=0$,\color{black}{\text{How many times will ...
1k views

### Rearrange words to make a sentence

The following puzzle is from the October 1961 issue of the Eureka journal (published by The Cambridge University Mathematical Society): Rearrange the order of the following so as to make a true ...
5k views

### A Surprising Circle Packing

A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, ...
896 views

### Relatively prime numbers

Can you fill in the circles with numbers such that: Each pair of circles connected by one line contains relatively prime numbers Each pair of circles connected by two lines do not contain relatively ...