Questions tagged [combinatorics]

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

0
votes
2answers
63 views

It is not as Simple as it Looks to get the right Alignment

Of these US Coins (Quarter and Dime Combo). Initial arrangement of the coins as shown in the picture is as follows... Q D Q D Q D Q Objective is to attain the final configuration... Q Q Q Q D D D. ...
4
votes
2answers
286 views

How many codes are possible?

The line - codes we are looking at consist of black and red lines. These lines can have width 1 or 2. Black and red lines are taking turns, black line, red line, black line, ... The code ends and ...
4
votes
2answers
259 views

5 cars in a roundabout traffic

Five cars are driving in a roundabout traffic at the same moment. Each comes from an other direction, and drives less than one full round. Also each car leave the roundabout traffic in an other ...
4
votes
1answer
68 views

A Prime Length Rope into Prime length ropes

We have a rope with a prime unit length, and we need to divide this rope into $9$ ropes by cutting it with prime and/or 1 unit lengths. After cutting the rope, you are supposed to find any kind of ...
6
votes
2answers
238 views

Savage Road Signs (Part 3)

You only need to have read Part 1 to understand this question, reading Part 2 will only help understanding the epic storyline. Your daughter refuses to talk to you even though you have (once more) ...
14
votes
7answers
528 views

10 coins, 3 of them are fake

Inspired by some great weighing puzzles here (This being one of my favorites), I just made another weighing puzzle - I'm not quite sure how difficult or easy this one is. You are given 10 coins, 7 of ...
12
votes
3answers
472 views

How many possible starting positions are uniquely solvable for a nonogram puzzle?

This type of puzzle goes by many names: Nonogram, Picross, and Griddlers are all mentioned on the Wikipedia page, Simon Tatham calls it Pattern, I was introduced to it as Descartes Rainbow, ... The ...
0
votes
0answers
99 views

A series of blocks (total $n + m$) is given to us and 0 is stored initially in each.We are given a number $H$ and we can choose $H$ blocks at a time [on hold]

Operation - we can choose $H$ blocks at a time and can fill those blocks with digit 1. we can do this Operation as many times we want. if block has already 1 in it and we are going to put 1 again then ...
7
votes
4answers
271 views

Savage Road Signs (Part 2)

Please read part 1 or this might be confusing Since part 1, you have replaced the stolen stickers and your daughter has forgiven you. The highway ended up being a full 700km long, so you are happy ...
2
votes
3answers
188 views

16 people, make 3 consecutive round of 4 players

I am struggling with this issue for a tournament I am planning. Take 16 people. Consider a 4-player game. To be clear, in each round all 16 players must play the game once. I want to make at least 3 ...
22
votes
4answers
2k views

Savage Road Signs

There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker ...
2
votes
2answers
1k views

Finding numbers having exactly two distinct digits

We have $10^K$ road signs (numbered 0 through $10^K−1$). For each valid $i$, the sign with number $i$ has the integer $i$ written on one side and $10^K−i−1$ written on the other side. We need to ...
33
votes
9answers
4k views

Winning Strategy for the Magician and his Apprentice

There are $13$ upside-down opaque cups and $2$ balls, a magician and his apprentice and yourself. You decide under which cups to put the balls, and the objective of the magician is to find the two ...
7
votes
6answers
801 views

Restoring order in a deck of playing cards (II)

Michelle has a deck of 52 playing cards in a pile with their backs facing up. She takes the first 2 cards in the pile, turns them over, and places them at the bottom of the pile. She now takes the ...
13
votes
3answers
2k views

Restoring order in a deck of playing cards (I)

Michelle has a deck of 52 playing cards, stacked in a pile with their backs facing up. She takes the first 2 cards in the pile, turns them over, and places them at the bottom of the pile. She now ...
7
votes
2answers
171 views

A Guide to the Number Rotation Puzzle

This is an extension of What is the strategy to solve Simon Tatham's Twiddle? in that it explicitly goes beyond the default gamemodes of Twiddle The Number Rotation Puzzle (NRP) is a combination ...
37
votes
2answers
4k views

Pirate democracy at its finest

With our pirate crew becoming too big, the captain grew very concerned about splitting all the treasure - we continued to split it equally, but, of course, each crew member got less and less with the ...
6
votes
5answers
319 views

How to Modernize Student Council

You are the math teacher at a high school and you are in charge of organizing Student Council for the whole school next year. Your boss, the Principal, read a research paper on Student Councils and ...
13
votes
2answers
604 views

Picking coins from two piles

It is a variation of the game of Nim. The rules are : The game is played with two piles of coins. Initially, the first pile contains N coins and the second one contains M coins. There are two ...
19
votes
6answers
2k views

My Sixteen Friendly Students

I have sixteen students in my class who sit in four rows of four. Each week they sit in a different order. After a number of weeks every student has sat next to every other student, next meaning ...
5
votes
1answer
127 views

Surviving the Zombie Apocalypse

It is the zombie apocalypse. Your car has limited fuel in it, and you will not be able to refill your tank once you run out. You are planning one final mission to gather supplies. You have identified ...
3
votes
2answers
190 views

What is the fewest amount of clicks needed to create a tier 5 tile?

PLEASE NOTE! A different problem that uses this same ruleset that can likely only be solved with brute force and a computer program has been posted to math.se, viewable HERE. I was unaware of the ...
-4
votes
1answer
97 views

Unlock My Phone! November 2018

I had a bit of phone trouble last year, so I had to take a break from puzzle passwords. But once I got it working again I hopped right back in, although this is a pretty easy one. What is my phone's ...
19
votes
5answers
1k views

Island of Knights, Knaves and Spies

There is an island with $N$ inhabitants (for example $A_1, A_2, \dots, A_N$), each of them is either a knight, a knave, or a spy. As usual: knights will always tell the truth upon answering a ...
17
votes
3answers
2k views

France's Public Holidays' Puzzle

In France, there are 11 public holidays. As a French employee who enjoys public holidays on week days, you want to know if it is possible that all of the 11 public holidays during one year fall on ...
1
vote
2answers
202 views

Sequence made of symbols

(My friend in real life gave me this)That's the original sequence: ⬅↕➡,⬅↕,➡,⬅,?,?,↕➡ I'm going to use other symbols to make it readable: (/), (/,), (/, ?, ?, /) I've noticed that the comma ...
1
vote
2answers
128 views

alphanumerical sequence Correct one

I have tried to solve this sequence which, I suppose has been created from the combination of a,b,c,d,e. I've reposted the correct sequence The sequence: (a,c), ?, ?, ?, (a,e), ?, ?, (c,d), ?, (b,...
5
votes
1answer
151 views

Dragons and Dragon Slayers

In the Kingdom, there are 7 dragons and 7 dragon slayers. Each dragon has ($\text{index}\times10000$) hit points (i.e. $10,000\to70,000$). Each dragon slayer does ($\text{index}\times1000$) damage (i....
30
votes
8answers
2k views

Wolves and sheep

All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one ...
4
votes
2answers
624 views

Bridge building with irregular planks

Imagine you have a big rectangular pond in your back garden. You wish to build a bridge from your house in the lower left corner to the small pagoda in the top right. You have lots of planks of ...
12
votes
1answer
810 views

Hacking a Safe Lock after 3 tries

My friend has a safe lock, with a numeric password of 4 digits (varying between 0-9 each). She lost the password and looked for my help. Fortunately, I was able to hack it. I could try some different ...
3
votes
1answer
221 views

Albrecht Durer Inspired Magic Square

A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n ...
16
votes
3answers
2k views

Four buttons on a table

I was asked lately (in an interview) to solve this puzzle, which is similar to the 4 cups on table puzzle. In a certain room there is a rotating round table, with 4 symmetrically located ...
0
votes
2answers
116 views

Chess tournament winning streaks #2

So I asked a question here, which asks how many ways there are to score 7 points in 7 chess tournament games using the system on lichess.org, outlined both here and in the original question. That was ...
6
votes
7answers
315 views

Find minimum number of meeting periods to reach 2 degrees of separation for a group [closed]

I am running a training course and I want to arrange a set of 1:1 meeting periods between the participants such that at the end of the day there is a maximum of 2 degrees of separation between any of ...
9
votes
1answer
289 views

Chess tournament winning streaks

On lichess.org, they use a points system for keeping track of who is winning in a tournament. A win is worth two points, a draw is worth one point, and a loss worth zero points. Once a player has ...
3
votes
4answers
2k views

Move fast … Or you will lose

Suppose you're on a 4 × 6 grid, and want to go from the bottom left to the top right. How many different paths can you take? Avoid backtracking -- you can only move right or up.
2
votes
2answers
245 views

Unlock an answering machine using minimum number of digits

You know of answering machines with a remote inquiry facility, where you can call the answering machine and enter a four digit passcode into your telephone keypad, so you can listen to your messages ...
7
votes
2answers
2k views

Rectangles in a chess board

How many rectangles can be made from the individual spaces of a chess board?
11
votes
4answers
305 views

Distinct Arrangements of Balls on Tiles

You want to put several balls on $8 \times 8$ tiles, such that all $16$ ball arrangements on its rows and columns are different. What is the minimum number of balls to be put? Two arrangements of ...
3
votes
2answers
248 views

Enumerate the ways of putting six armies of queens on a humongous chessboard

This is a sort of a sub-problem of the open puzzle Peaceful Encampments, for high numbers of armies. Consider a chessboard with an astronomically large number of vanishingly small squares, on which ...
4
votes
2answers
164 views

Proving the count of symmetric configurations of pentagon

In a 3 × 3 dot grid, there are 5 configurations of symmetric pentagons. I am confused about how to prove that it is really just 5. Can anyone enlighten me?
9
votes
4answers
407 views

Breaking Balance (Part C)

For a starting number of otherwise identical coins there are among them TWO IDENTICAL counterfeit coins which are either heavier or lighter than the rest. Using a three-pan balance (described in ...
2
votes
0answers
90 views

Telephone Exchange Vandalism [closed]

Our telephone exchange has 1000 wire-based connections. You dial a number, you get connected to the exchange and they put you through. Yesterday, vandals broke in and disconnected all the wires. Your ...
3
votes
1answer
108 views

Find a specific path on an n x n grid [duplicate]

Given a puzzle of the following form: Find a path between the top left corner to the bottom right corner, visiting each spot (.) exactly once. You can only move horizontally or vertically. ...
5
votes
2answers
192 views

Rotating 12 players on 2 tables

I'm stuck trying to find a good way to rotate 12 poker players on 2 tables. Assumptions: There are 12 players There are 2 tables We play for 4 hours Playing with sb means sitting at the same table ...
3
votes
3answers
1k views

Three coins for the fair king [duplicate]

Based on the question Eight coins for the fair king: I saw a comment saying "There isn't a good solution known even with three coins in all cases". So the challenge here is to try to solve the same ...
14
votes
4answers
571 views

Balancing Balls

I have a disk with 6 equally spaced dents around the edge. The disk balances on the center point. I want to place marbles around the edge so that it stays balanced. There are four ways that this can ...
12
votes
4answers
799 views

Crosses and Circles

Place two crosses on two cells of each row and column of this 9×9 board, and circles elsewhere, so that the number on the right of each row indicates the number of circles between its two crosses, ...
8
votes
2answers
664 views

Four Magic Ellipses

These four ellipses represent four sets and all the possible ways they can intersect (a Venn diagram, in other words). There are 8 regions inside each ellipse, and 15 regions altogether. Is it ...