🔄 Patterns & Sequences
Spot repeating cycles and predict what comes next
🔄 What are patterns?
A pattern is anything that repeats in a predictable way. Once you spot the pattern, you can predict what comes next — even hundreds of steps ahead.
🎡 Rotation patterns
When something rotates, it eventually comes back to where it started. A paper divided into 6 parts rotated by 1 part each time returns to its original position after 6 rotations.
So after 8 rotations: 8 ÷ 6 = 1 remainder 2. That means 8 rotations = same as 2 rotations.
⚽ Circular passing
11 players in a circle, passing to the 3rd person on the left. Starting from player 1:
1 → 4 → 7 → 10 → 2 → 5 → 8 → 11 → 3 → 6 → 9 → 1 (back to start!)
Everyone gets the ball exactly once before it returns. The key insight: since 3 and 11 share no common factors, the ball visits all 11 players.
📝 Repeating digit patterns
Writing "2025" over and over: 2,0,2,5,2,0,2,5,2,0,2,5...
The pattern repeats every 4 digits. To find the 100th digit: 100 ÷ 4 = 25 remainder 0, so it's the last digit in the cycle = 5.