MatMod logo

Puzzles

Chess Puzzles      Exercises      Logical Puzzles      Network      Production      Simple Puzzles      

Progressive Party Problem (party)

This problem was originally stated by Peter Hubbard (Southampton University), organizer of the yacht rally of 42 boats and their crews. A important evening event in the yacht rally is to organize a party where each crew socializes with as many other crews as possible. Some of the boats are selected to serve as “host boats” where the party takes place, the other boats are the “guest boats”. The crews of the host boats stay on their boats for the whole party, while the crews of the guest boats visits the host boats. In order to socialize as much as possible, the guest crews only stay for 30 minutes at one host, then they visit another host boat. The whole party lasts 3 hours.

Read more

The Social Golfer Problem (golfers)

In a local golf club, there are 16 social golfers, each of whom plays golf once a week, and always in groups of 4. Find a schedule of 5 weeks, such that no golfer plays in the same group as any other golfer on more than one occasion, if it exists. If it does not exist, then find a schedule of “maximal socialisation”, that is, as few repeated pairs as possible. (Found at: http://www.csplib.org/Problems/prob010/).

Read more

Sum of Unit Fractions (fractions)

There seems to be no efficient method to solve these two problems. So, before solving them, let’s pose another problem that is linked to them: The problem is to find the smallest number n (the largest unit fraction ) in Egyptian fraction expansion for the number 1, that is, find a and n, with n as small as possible with a ≤ n, such that:

Read more

Packing Circles in a Square (I) (circles)

Find the maximum diameter of n mutually disjoint circles of equal size – that means, they must not overlap each other – inside a unit square. (“Inside a unit square” means that all circles must be completely inside the unit square (see [1]).

Read more

Mastermind Game (mastermind)

Mastermind is a code-breaking game for two players, the codemaker and the codebreaker. The game is played on a decoding board (see Figure 1), containing various rows (7 rows in Figure 1) of four large holes on the left, and four smaller holes on the right hand side. At the bottom there is a row of 4 shielded large holes.

Read more

Creating a Perfect Maze (maze)

A (2-dimensional, rectangular) maze is a grid structure consisting of m × n cells. Each cell is surrounded by at most 4 walls. A wall separates two neighboring cells. If the wall is missing then they are linked by a direct path (from the first cell we can step into the second without piercing a wall).

Read more

Path in Labyrinth (labyrinth)

Given a labyrinth consisting of white and grey cells. The white cells can be used in a path, and the grey cells are “walls” that are obstacles. The two red cells are the entry and leaving point of the labyrinth. Find the shortest path connecting the entry with the leaving point. If there is no path then find the path that pierce the least possible “walls” (see Figure 1).

Read more

Crucipixel Game (crucipixel)

Given a m × n grid, the purpose of the game is to darken some of the cells so that in every row and every column the darkened cells form distinct block of the lengths and in the order prescribed by the numbers on the left of the row and on top of the column.

Read more