About

Culica Culica is a puzzle and a multi-player game played on the surface of a 3×3×3 cube. It consists of a cube base an pegs of four different colours that click into the cube. There are many different games and puzzles that can be played on this board. If you have two or more Culicas, then you can even connect them together with the pegs to make a larger playing board. Each face of the cube consists of a 3×3 square, so there are 6·9 = 54 playing locations. Every location has exactly 4 neighbouring locations, some of which may lie on a different face of the cube. I will not describe all the different multi-player games that are possible, and restrict myself to some of the more interesting solo puzzle tasks. CuColours: Fill the whole cube with pegs such that pegs of the same colour are never neighbours, nor diagonally adjacent. Jump to solution CuSnakes: Find a snake's tour on the cube. Place the first peg somewhere on the cube. Each subsequent peg must be adjacent to the previously placed peg. Try to place as many pegs as you can before no more moves are possible. It is possible to fill the whole cube this way. If you have done that, try to make it so that the final peg is adjacent to the starting peg (for which you can use a different colour peg so as to keep track of it more easily). Jump to solution CuFrog: Find a frog's tour on the cube. This is like the snake's tour, but using 'frog' moves. A frog moves exactly two squares straight in any direction (but not diagonally). So between two consecutive pegs you place must lie exactly one other square, which may be empty or full. Again try to fill as many squares as possible, preferably such that the final location is a frog's move away from the first. Jump to solution CuKnights: Find a knight's tour on the cube. Place the first peg somewhere on the cube. Each subsequent peg must be a chess-knight's move away from the previously placed peg, that is to say that it goes two squares forward in one direction and then one square sideways (at right angles to the forwards direction). You are only allowed to go from one face of the cube to another at most once per move. An easier way to understand this is to imagine a 2x3 rectangle wrapped around the surface of the cube, and a knight move goes from one corner of this rectangle to the diagonally opposite corner. Try to place as many pegs as you can before no more moves are possible. It is possible to fill the whole cube this way. If you have done that, try to make it so that the final peg is a knight's move away from the starting peg, so that you have a 'closed' knight's tour. Jump to solution CuMadness: Place as many pegs as you can using the following rules: Every red peg must be next to exactly one yellow peg, no more no less. The colours of its other neighbours do not matter, and can be any number of red, green or blue. In the same way every yellow must be next to exactly one green, every green next to exactly one blue, and every blue next to exactly one red. This is remarkably difficult. Jump to solution CuRing: Place as many pegs as possible such that for every peg there is no peg of the same colour within the next three squares in any of the four directions. Two pegs of the same colour may be close together diagonally, but if they lie in a straight line, then there must be at least three squares between them. Jump to solution CuLoops Consider the loops of squares around the cube - a loop of 12 squares in a straight line going around four faces of the cube. There are 9 of such loops. Fill as much of the cube as possible with the four colours of pegs such that no loop has more than 3 pegs of the same colour. Note that this means that if a loop is to be completely filled it will have exactly three of each colour. Jump to solution CuLook: Similar to CuLoops, but using a single colour. Place as many pegs as possible such that every loop has at most one peg. Then try again such that every loop has at most two pegs. Then try with three, with four, etc. Jump to solution CuWizard: Consider four squares in a row, adjacent to each other, and crossing over an edge of the cube such that two squares are on one face and two squares on another face of the cube. There are 36 of these quadruplets on the cube. Put pegs on the cube such that as many of these quads as possible contain four pegs, one of each colour. Jump to solution CuNitrogen: Find a molecule consisting only of Nitrogen atoms, that is to say place pegs such that every peg has exactly three neighbouring pegs leaving its fourth adjacent location empty. Apart from the trivial empty cube, there are only two solutions. Jump to solution CuOxybon: Find molecules consisting only of carbon and oxygen atoms. In other words, place red pegs ('Oxygen') such that they have exactly two neighbouring pegs and two neighbouring empty locations, and pegs of any other colour ('Carbon') such that they have four neighbouring pegs. A completely filled cube would be a valid molecule containing only carbon, so let's use only molecules that have at leasy one Oxygen atom. Fill up as much of the cube as possible using one or more of these molecules that contain at least one red peg. Jump to solution CuOxygen: Find a molecule consisting only of Oxygen atoms, that is to say place pegs such that every peg has exactly two neighbouring pegs leaving its two other adjacent locations empty. Use as many pegs as possible to create one or more of these molecules. Jump to solution CuSol: Solitaire. Fill the whole cube with pegs, except for any single square. Then try to do as many moves as possible, where a move consists of jumping one peg over an adjacent peg to an empty square immediately behind that, and removing the peg that was jumped over. So each move involves three adjacent squares in a row, which start full/full/empty before the move and are empty/empty/full afterwards. Each move removes one peg, so try to do 52 moves so that only one peg remains. Jump to solution You can find these and other puzzle tasks on the Culica site. If your browser supports JavaScript, then you can play these Culica puzzles by clicking the link below: