The (Final) countdown

TL;DR

This paper provides a comprehensive analysis of the Countdown game, including complexity, algorithms, and enhancements, aiming to deepen understanding and challenge both human and computer players.

Contribution

It introduces a new algorithm that significantly speeds up game resolution and explores ways to increase game difficulty and complexity.

Findings

New algorithm increases resolution speed by a factor of 20

Analysis shows the game has high computational complexity

Proposes modifications to make the game more challenging and potentially undecidable

Abstract

The Countdown game is one of the oldest TV show running in the world. It started broadcasting in 1972 on the french television and in 1982 on British channel 4, and it has been running since in both countries. The game, while extremely popular, never received any serious scientific attention, probably because it seems too simple at first sight. We present in this article an in-depth analysis of the numbers round of the countdown game. This includes a complexity analysis of the game, an analysis of existing algorithms, the presentation of a new algorithm that increases resolution speed by a factor of 20. It also includes some leads on how to turn the game into a more difficult one, both for a human player and for a computer, and even to transform it into a probably undecidable problem.