# 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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### Mice and their relations

In a colony of $(m n+1)$ mice, must at least one of the following statements be true? If so, why? There is a set $A$ of $(m+1)$ mice none of which is a parent of any other in the set. There is an ...
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### Find all solutions to a sum of fractions

Find all the solutions to: $$\frac{1}{x}+\frac{2}{y}-\frac{3}{z}=1$$ where $x, y, z$ are positive integers.
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### How high does the ladder reach up the wall?

A ladder of length $l$ rests against a vertical wall. Suppose that there is a rung on the ladder which has the same distance $d$ from both the wall and the (horizontal) ground. Find explicitly, in ...
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1 vote
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### What size square grid can you tile?

A tiling of an n × n square grid is formed using 4 × 1 tiles. What are the possible values of n? A tiling has no gaps or overlaps, and no tile goes outside the region being tiled.
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### Show there is always a pair at least 16 apart

The integers 1 to 4 are positioned in a 6 by 6 square grid as shown and cannot be moved. The integers 5 to 36 are now placed in the 32 empty squares. Prove that no matter how this is done, the ...
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### A simple number sequence puzzle

This is a simple number sequence puzzle, you are given 6 related number sequences, observe them, find the pattern; Your task is to give the first sixteen terms in the seventh sequence. 1d5, 2d3, ...
363 views

### Determine the highest possible sum of all faces of cube

There is a non-negative integer written on all six faces of a cube. Integers on all possible three common adjacent faces (all faces are adjacent to each other) are multiplied and then they are added. ...
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### Tic-Tac-Collatz

Have you ever heard of the Collatz conjecture? Just in case you haven't, I'll summarize it for you! Take any positive integer $n$, if it is even then simply divide it by $2$; however, if it is odd, ...
• 10.5k
1 vote
242 views

### 4x4 grid with the shortest longest path

This is an extension of this beautiful puzzle. This time your task is to find the hardest 4x4 grid. In particular, find a 4x4 grid containing every number from 0 to 9 at least once, such that the ...
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### Find out the longest path being alive [closed]

Start from any integer. Move horizontally or vertically (not diagonally), and if you come across the same integer more than once you will die. Moving diagonally is not allowed. What is the longest ...
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262 views

### Can the Bomb squad succeed?

A bomb squad consisting of three members, person C had to defuse the bomb while other members (A,B) had the task to detect the bomb. The bomb squad was summoned to the bank to defuse 2 bombs located ...
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