How many ways are there to split the numbers 1, 2, 3, 4, 5, and 6 into two groups, such that the product of the numbers in one group is 24 and the sum of the numbers in the other group is 12? An answer should enumerate all of the possibilities (if any) and prove that there are no others. (It's po...

Professor Devonshire was losing his marbles, Dr. Wallaby thought, staring at the equations filling the board in Dr. Devonshire’s office. What kind of addition was this? 1+1 = 6 2+1 = 6 1+6 = 6 2+6 = 6 6+6 = 6 1+3 = 8 7+9 = ? I wonder what goes in the blank?

In a grid rectangle $20210 \times 1505$, two diagonals are drawn, and all the cells containing segments of diagonals are painted. How many cells are painted?

Several plants and zombies (no more than 20 creatures in total) came to the party “Plants VS Zombies”, and it turned out that all the creatures are of different heights. When a plant speaks to a lower creature, it tells the truth, and speaking to a higher creature, it lies. Zombies, on the other ...

Recently I rewatched "A Beautiful Mind" based on the life of the American mathematician John Nash. And the other day I came across a book spread photograph, in which one attentive reader connected exclamation marks, !, and got a certain figure (red lines). Do anyone used such approach as puzzl...

Your task is to solve the Sudoku and complete the missing words in the following poem. Classic Sudoku: Each row column and box contains the digits 1-9. XV-rules: Digits separated by V must add to 5. Digits separated by X must add to 10. There is no negative constraint (e.g. a 3-7 domino can appe...

What is a minimum number of $1\times 3$ tiles that can be put on a table $5\times 5$ so that no more tiles $1\times 3$ can be put on it? It is 5 but I can not prove that if we put 4 tiles there is still room for one more.

A rectangle of size 2021 × 4300 is given. There is a billiard ball at some point inside it. It is launched along a straight line forming an angle 45◦with the sides of the rectangle. After reaching a side, the ball is reflected also at angle45◦; if the ball enters a corner, it leaves it along the s...

I've always been fascinated Conway's Game of Life, but one thing that always bugged me was the idea that a cell could live forever. There are alternate rulesets (e.g., Generations) which address the aging issue, but they address it by making a cell's lifespan even longer; much like Shakespeare's ...

I am of the order of the valiant Knights of the Square Table, an elite fraternity—far more so than those so-called Knights of the Round Table. There are so many of them, but only two of us. I serve my lord the King. We are at war. His Majesty’s mortal enemy has come to us on a most unusual diplom...

The words bellow are in hierarchical order based on their relation to a word. Apex is the most elite one. apex fix mix sex What is the related word and why?

Why are mathematical question posted on Puzzling SE? Is Mathematics SE not good enough? Here are some examples: A circle touches two sides of a triangle and two of its medians A geometric puzzle. What is the angle? All wrapped in functions and so on. All those are classical math questions and t...