# Questions tagged [combinatorics]

A puzzle based on combinatorial mathematics, which is the study of finite or countable discrete structures.

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### Lots of Parallelepiped

A,B,C,D are four points which are not on the same plane. How many different parallelepiped can be constructed whose vertices are these points? Parallelepiped is a solid figure with six faces ...
801 views

### Sticky sticky stick stick

You are given a long enough stick. Your task is to create a new type of foldable ruler something like shown below with it by cutting the stick into pieces and folding them at one point: You need to ...
416 views

### Rectangular Prisms

Eight corner bricks are taken out from a 5x5x5 block, which is something like below: How many rectangular prisms of all sizes can be counted in this block? Source: Oyun 2018 Final Exam Question
254 views

### Oddy Chessboard

On a standard chessboard, What is the number of different arrangements of pawns such that every square has an odd number of pawns on its neighbor (horizontally or vertically) squares? Note: ...
201 views

### Mathematical formulation for Dr. Eureka

I have to prepare an algorithm to solve the puzzle part of Dr. Eureka, a multiplayer game from Blue Orange Games. This is part of a research project that also involves computer vision and robotics. ...
337 views

### Rectangles and Diagonals

A 4×4 table has 18 lines, consisting of the 4 rows, the 4 columns, 5 diagonals running from southwest to northeast, and 5 diagonals running from northwest to southeast. A diagonal may have 2, 3 or 4 ...
153 views

### Permuting rows and columns to switch white rooks with black rooks

An adversary places eight white rooks and eight black rooks on sixteen squares of a chessboard, subject to these rules: In any row, there must be exactly two rooks, one of each color. In any column, ...
464 views

### 6 nails String Art

String art is an arrangement of thread strung between nails to form geometric patterns or representational designs such as a ship's sails, sometimes with other artist material comprising the remainder ...
444 views

### A simple puzzle about moving students

You have n students sitting in a line and you want to move them so that no student is sitting next to anyone they were originally sitting next to. What is the ...
420 views

### Covering an 8×8 grid with trominoes

I tried to find non-trivial solutions on a deficient 8×8 grid covered with trominoes and I regret to say that after extensive efforts I found only two non-trivial solutions: The conditions of ...
1k views

### Lego brick towers

Disclaimer: I'm honestly not sure whether this question is best placed at Puzzling, Maths, or Programming SE, but I'm interested in the best solution, and I'm sure mods will shift the question around, ...
562 views

### Magic-preserving Permutations on a 4x4 Magic Square

Messing around with some magic-square puzzles, I faced the problem of deciding whether some two magical squares are, in fact, the one and same square wearing a different hat. It seemed to me, that for ...
546 views

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### Put combinations of symbols, so the result will have the same numbers of As, Bs and Cs

Put combinations of symbols A, AA, AAB, AABB, AABC, AAC, ABB, ABC, AC, B, BB, BC, and C to each circle, in such a way that the symbols in each row with 3 or 4 circles in all three directions, have the ...
377 views

### The most probable key

You broke into John Doe's house and found the safe. It has a combination lock with 4 dials ranging from 0 to 9 each. ...
992 views

### Possible pawn combinations

This may seem simple, but I have a problem calculating it. It may be because it's Monday morning. How may possible valid combinations of one color pawn (white or black, your choice) positions are ...
441 views

### Cover all squares in a square grid by moving to adjacent squares

Admittedly this is a problem I encountered from school but I cannot think of a proper proof solution. I thought about the logic that in order to cover all squares, there must be closed loops of ...
230 views

### Interesting card combinations [closed]

In a normal pack of playing cards (without jokers), the probabilities of the following events are the same: (1) Drawing a set of 4 different cards (irrespective of its color and suit) - let us call ...
364 views

### Jigsaw Logic: ?s galore

I am working on a 256 piece jigsaw puzzle, but I am having a lot of trouble. Instead of the picture being a landscape or painting, the final image is just a sixteen by sixteen grid of identical ...
170 views

### Arrange six cigarettes in such a way that each cigarette touches every other cigarette [duplicate]

What are some ways to arrange six cigarettes in such a way that each cigarette touches every other cigarette?
194 views

### 15 pawns on a chessboard

15 pawns are placed on the centers of distinct squares of a chessboard. Prove that there are three pawns which form a right triangle. In the example board below, a couple of right triangles are ...