Kaprekar's Constant: Why Four-Digit Numbers Reach 6174

Kaprekar's Constant pulls almost every four-digit number to 6174. Why does this simple digit routine have such a powerful trap? Kaprekar's routine sorts four digits, reverses them, and subtracts—and almost every valid starting number eventually reaches the same fixed point. The animation compresses thousands of numbers into just 54 gap states, revealing a single funnel toward 6174. Column-by-column borrowing explains why those gap states control the digits that appear next. A comparison with the three-digit routine shows why the number of digits changes the destination. Chapters: 0:00 The 6174 Number Trap 1:34 When Order Disappears 3:20 Just 54 Possible States 4:50 One Unavoidable Funnel 6:42 How Borrowing Shapes Digits 8:15 Why Four Digits Matter 9:53 What 6174 Really Represents #KaprekarsConstant #NumberTheory #MathAnimation