Trilogic Game

The Trilogic game was a game played by the First Doctor and the Celestial Toymaker. The Celestial Toymaker gave the Doctor only 1023 moves to finish the game, or he would be trapped in the Celestial Toyroom forever. The Doctor used voice control to place the last piece. (TV: The Celestial Toymaker)

Rules
The rules were as follows: There was a tower made up of 10 plates, each one smaller than the one it was on top of, forming a pyramid-like shape.

There were three spaces, A, B, and C where the pieces could be moved. The goal was to move the entire stack from A to C. However, only one piece might be moved at a time, and a piece might not be placed on top of one smaller than it. (TV: The Celestial Toymaker)

Behind the scenes

 * The Trilogic game is a variant of the puzzle. 1023 = 210 - 1 moves is the minimal number of moves necessary to solve the puzzle for 10 pieces.
 * Once filming on The Celestial Toymaker was completed, the prop was given to actor Peter Purves (Steven). However, unable to get further acting work, he came to see the prop as the source of his bad luck. After eighteen months in his possession, he threw it out, and the very next day was offered a role in the police procedural series Z-Cars.