# Puzzles

## Florian's Fishes

Florian's Fishes is a puzzle in which each piece comprises two squares plus four equilateral triangles. This puzzle uses the full set of 49 distinct pieces.

In other tessellations (tilings) of the plane, mathematical methods can be applied in helping to derive solutions. This does not appear to be the case for solving Florian's Fishes, which probably demands trial and error methods. This kind of puzzle can be quite challenging for experienced puzzlers.

The puzzle board looks like an ocean (blue) with a dolphin and two fishes.

## Dolphy Puzzle

 Dolphy puzzle is a variant of Florian's Fishes in which pieces comprise two squares plus four equilateral triangles. This puzzle use only six pieces from the full set of 49 pieces which covers all possible arrangements. In all other tessellations (tilings) of the plane, mathematical methods can be applied in helping to derive solutions. This is not true for Dolphy puzzle which relies entirely on trial and error. This kind of puzzle can be quite challenging, even for children. Do not use computers! This does not make any sense.

## Mechanical Puzzles

Mechanical puzzles are those with moveable, though constrained, objects ...

Logic Cube with Balls (Falling Marbles) is one of the most simple mechanical puzzles known. The puzzle is a transparent cube containing 26 balls. There is an empty space (the place of the missing ball), which makes it possible to roll the balls inside the cube.

4x4x4 Logic Cube is a far more daunting challenge than the 3x3x3 cube. The number of pieces is far greater, and there are no "fixed" pieces to serve as a reference.

These puzzles are a challenge for anyone!

## 3D Logic Games

The 3D logic games can be played by two or more players who place pieces, one by one, in ducts (holes), or on sticks, or directly on the game board in order to obtain horizontal, vertical or diagonal lines of the same color. The winner will be the player who makes the most such lines.

## 3D Puzzles - same volume and different shapes polyhedral pieces

Most of puzzles in this group comprise polyhedral pieces with the same volume but different shapes. If two pieces have the same shape then their color is not the same. The pieces are generated by cutting a regular polyhedron - such as a cube.

## 2D Puzzles generated using a tessellation of the plane

Many 2D Puzzles are generated using a tessellation of the plane.

The word "tessellate" means to form or arrange polygons in a checkered or mosaic pattern. It is derived from the Ionic version of the Greek word "tesseres", which in English means "four". The first tilings were made from square tiles.

A regular tessellation means a tessellation made up of identical regular polygons. Only three regular polygons completely tessellate (cover) the Euclidean plane: triangles, squares and hexagons.

A semiregular tessellation uses a variety of regular polygons. The arrangement of polygons at every vertex point is identical.

In tessellations (tilings) of the plane, mathematical methods can be often applied in helping to derive solutions. This collection of puzzles demonstrates this is not always true.