Peg-in-Cube Puzzle

The holes create 125 internal volumetric units within the cube. Depending on its length, a peg closes off two, three, or four of these units. There are 14 pegs each of lengths two, three, and four. This totals a volume of 126 volumetric units. Therefore, it is not possible to insert all 42 pegs into the cube. In the best-case scenario, one peg of length two will remain.

The holes and pegs are designed with a slight taper. With a little pressure, the peg can be secured in the cube so it doesn't fall out immediately.

The pegs are usually printed in different colors so that one can see how many units they occupy. The first picture shows the cube with white pegs of length two, blue pegs of length three, and red pegs of length four.

To increase the difficulty of the puzzle, all pegs can also be printed in the same color. The second picture shows the cube and all 42 pegs in the same color.

Game Idea for Two Players

Each player receives half of the pegs of each length. Players then take turns inserting pegs into the cube. The round ends when both players can no longer fully insert any of their remaining pegs into the cube. The sum of the lengths of the remaining pegs equals the penalty points for that round. The player with the fewest penalty points at the end wins.

In an optimal game, one peg of length two will remain at the end, as all pegs together consume more volume than is available inside the cube.

Solitaire Game

If you want to solve the puzzle as a single player, you set aside one peg of length two at the beginning and then try to insert all other 41 pegs into the cube. The last picture shows a solution without revealing too much, as all pegs are the same color.

It is easier than it might seem at first glance to insert all 41 pegs. That's why it's more fun to play with two people, as you have to develop strategies to block your opponent without being blocked yourself. It is thus similar to Connect Four or Nine Men's Morris, but in three dimensions.