Brute Forcing The Countdown Numbers Game - Computerphile

TL;DR

Teaching programming using the Countdown Letters Game inspired a programmer to brute force all possible combinations of the Countdown Numbers Game, leading to interesting statistics and insights.

Transcript

we are going to look at the countdown numbers game so i used to teach uh programming and i used to teach the countdown letters game and that worked out quite well i always liked teaching to the to the problem not at all so it was quite nice to have that focus of the countdown latest game and i was always thinking next year i'll do the numbers game ... Read More

Key Insights

• #️⃣ The easiest numbers to make in the Countdown Numbers Game are 100, 102, 104, and 108.
• #️⃣ Certain board number combinations cannot reach a target number over 100.
• 🎯 Even target numbers are easier to make than odd target numbers.
• ❓ Brackets were eliminated in the solution, simplifying the calculations.
• 😃 Combining too many big numbers or too few can affect the solvability of the game.
• #️⃣ There are 1226 sets of board numbers that can solve any target number between 100 and 999.
• #️⃣ The hardest number to make in the game is 947, which requires a larger set of board numbers.

Questions & Answers

Q: How does the Countdown Numbers Game work?

In the game, players choose six numbers and must use mathematical operations to reach a target number between 100 and 999.

Q: What are the rules and limitations of the game?

Players can add, subtract, multiply, and divide the chosen numbers, but concatenation and negative numbers are not allowed. Decimals are also not permitted.

Q: How did the programmer solve the problem of interpreting mathematical expressions correctly?

The programmer used reverse polish notation, where the order of symbols denotes how equations are solved. This ensured accuracy in interpreting the expressions.

Q: How did the programmer handle the large number of combinations?

The programmer used a cluster and distributed the computations across multiple instances to speed up the process. The calculations took a significant amount of time to complete.

Summary & Key Takeaways

• The Countdown Numbers Game involves selecting six numbers and using mathematical operations to reach a target number between 100 and 999.

• Brute forcing every possible game, the programmer simulated all combinations of numbers and operations.

• The solution utilized reverse polish notation and shuffled permutations to handle different mathematical interpretations.