Questions tagged [combinatorics]

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

Filter by
Sorted by
Tagged with
7
votes
3answers
130 views

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 ...
12
votes
3answers
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 ...
7
votes
3answers
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
6
votes
3answers
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: ...
6
votes
2answers
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. ...
3
votes
2answers
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 ...
7
votes
1answer
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, ...
11
votes
1answer
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 ...
10
votes
2answers
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 ...
15
votes
1answer
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 ...
10
votes
3answers
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, ...
5
votes
3answers
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 ...
13
votes
3answers
546 views

The $1 question: Tiling a triangle with trapezoids (the hard way)

Take a triangular grid consisting of 64 equilateral triangular cells in the shape of a larger triangle, and remove a single triangle at one of the tips. Can you tile this shape with 21 trapezoidal ...
3
votes
2answers
404 views

Lots of ships in the arbitrarily large battleship

This question is inspired by Oray's puzzle Lots of ships in the battleship. You have an $n\times n$ grid (a battleship board) and a certain number of $2\times2$ squares (ships) to place in the grid. ...
24
votes
7answers
6k views

Hacking an electronic keypad

You are a spy trying to break into an enemy facility. The back door is protected by an electronic keypad lock. You know that this particular lock is opened by a four digit code. Any stream of button ...
2
votes
5answers
555 views

Word game - possible to play all words?

You're trapped in a chamber and the only way out is to beat the chamber guardian on his own game: Word88. Both of you each take a turn to play a word. You can play one of the following: Add Play - ...
2
votes
1answer
247 views

Make lots of squares with only 6 squares

You are going to draw $6$ congruent squares to make as many squares as you can! What is the maximum amount of squares (except the original squares) you can create by drawing 6 congruent squares? ...
12
votes
4answers
503 views

2-Palindromic DNA

There are two bacteria. Both of their DNA sequences are only one letter long:  Bacteria #1 has the DNA sequence 'A'  Bacteria #2 has the DNA sequence 'T' Every minute, two things happen: ...
8
votes
4answers
432 views

A Treacherous Hobnob of Snobby Nobs

You are a lowly party planner, tasked with inviting some Nobs to a wedding dinner, and then seating them appropriately. Now, Nobs are very picky about their seating arrangement: they insist on having ...
14
votes
2answers
758 views

The Stubborn Tenant

A hotel is in the form of a grid that extends infinitely to the right and above, and a strange alien lives in the corner room. The proprietor wishes to vacate the six rooms closest to the corner, but ...
5
votes
2answers
189 views

Move 10 sheep on another shore [duplicate]

We have 10 sheep: 5 black and 5 white, two shores and a bridge through a river. 5 black sheep on a shore and 5 white sheep on another one. We have to move sheep on the opposite side. Sheep can move ...
16
votes
7answers
2k views

Soldiers in the Parade Ground

Twenty-five soldiers are standing in a parade ground consisting of a five-by-five grid of large concrete slabs, laid out in a neat north-to-south, east-to-west square array. Each soldier is standing ...
1
vote
1answer
157 views

Can all sums of a 5*5 matrix with the numbers {-2,-1,0,1,2} be different?

Is it possible to construct a matrix with 5*5 cells, where the value in each cell is taken from the set {-2,-1,0,1,2}, such that all of the 12 sums of the cells in each row/column/main diagonal have ...
8
votes
1answer
439 views

How many friends does Tiffany have?

Tiffany has 14 classmates; all of her classmates have a different number of friends in the class. How many of them are friends with Tiffany? (If A is a friend of B, then B is a friend of A.)
6
votes
2answers
233 views

Challenging 15 rectangle tiling problem

This will test you, a computer will definitely help. Just one set of $1:2$ aspect ratio rectangles this time, but $15$ of them. Short side only is listed. The challenge is to arrange them into a ...
5
votes
1answer
391 views

Unfair tiling puzzle

Your goal is to make two squares of the same size from a set of rectangles. Each of the rectangles has an aspect ratio of $1:2$. Select two sets of rectangles from the list: ...
4
votes
1answer
362 views

Hard tiling puzzle

Your goal is to make two squares of the same size from a set of rectangles. Each of the rectangles has an aspect ratio of 1:2. Select two sets of rectangles from the list: ...
4
votes
1answer
168 views

Slightly bigger 1:2 hand tiling, getting a little harder

Pretty sure an expert hand tiler would be able to find this. Please post a spoiler only if you hand tile it... Tile a $60\times60$ square with $1:2$ rectangles of sizes ...
4
votes
2answers
268 views

Trickier hand tiling

This should be a little trickier. Using $20$ rectangles of aspect ratio $1:2$, make two squares. Use sizes 2,3,7,12,16 in both squares. And split this list among ...
3
votes
1answer
116 views

Dissect a square into 1:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 and my 3:2 rectangle question) Tile a square completely with rectangles which have aspect ratio 1:2, integral side lengths and all different sizes. In other words selected ...
6
votes
3answers
250 views

Gimped Knight on a Torus

Place a knight on a toroidal $100 \times 100$ board (i.e. the edges wrap). Restrict his movement to a particular 2-square pattern (gimped from his usual 8-square pattern; for example, he may only be ...
7
votes
2answers
276 views

Dissect a square into 3:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 rectangle question) Tile a square completely with rectangles which have aspect ratio 3:2, integral side lengths and all different sizes. In other words selected from 2x3, ...
4
votes
3answers
569 views

Lottery in Minesweeper

The question is inspired by this scenario: In this case, we had 2 tiles remaining, and each had the equal probability of being a mine, based on the already deduced information. Thus it was necessary ...
3
votes
1answer
847 views

Is there a system to brute force a combination padlock?

Our escape room recently acquired some old lockers with a couple of these combination padlocks on them. Unfortunately, the seller didn't know the code. Is there a mathematical system in cycling ...
2
votes
1answer
178 views

Seven light bulbs in a circle, switch three adjacent ones at a time [duplicate]

You have seven light bulbs in a circle. All the lights are off and you want to turn them all on. You are allowed to switch the state of any three adjacent light bulbs at time. What is the minimum ...
3
votes
2answers
342 views

A Two-pan Non-Equal Arm Scale

There is a broken two-pan arm scale, consists of different weighed pans and different arm lengths. You are trying to weigh three different weights called X,Y,Z. You also know that the weights are ...
18
votes
2answers
2k views

True-False Examination

Alice, Bob, Chloe and David took a 10 question true-false exam; every correct answer of a question is $1$ point. Their answer sheet and the result is shown as below: So what is David's total ...
5
votes
2answers
1k views

Opening a safe by inputing a stream of numbers [duplicate]

Let's be given a safe that is secured by a code of length $n$ generated by using symbols from an alphabet of length $m$. Now a continuous stream of symbols may be entered in order to open the safe. ...
2
votes
2answers
311 views

A Shooting Target with 9 shots

You are a soldier in the army, and the commander is testing his soldiers for their shots. But the commander is also a mathematician and would like to test not only your shooting ability but also your ...
3
votes
1answer
132 views

Pawns and Discs

There are $8$ pawns next to each other and by using any size of discs you need to cover all pawns. The conditions while putting discs is that: Every disc and every pawn is called an object. There has ...
4
votes
1answer
114 views

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 ...
3
votes
2answers
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. ...
8
votes
3answers
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 ...
1
vote
2answers
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 ...
-3
votes
5answers
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 ...
12
votes
1answer
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 ...
0
votes
1answer
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?
5
votes
1answer
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 ...
22
votes
3answers
4k views

bored of eating soup

A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating. When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
1
vote
1answer
259 views

222 Black and 333 white balls [duplicate]

You have a bag with 222 black balls and 333 white balls in it. You also have an almost infinite supply of black and white balls that are not in the bag. You do the following over and over again: ...