Kaprekar's Constant

Real math is a lot more fun that the math that is taught in elementry school thru high school. Some number a really strange. One of the strangest is the number 6174, known as Kaprekar's¹ Constant.

Kaprekar's Constant (6174) will always be reached when you follow Kaprekar's Process:

1. Take any 4 digit number, using at least two different digits (numbers composed of all the same digits, such as 1111, will not work).
2. Arrange the digits in ascending and then in descending order. Add leading zeros if necessary. For example: 4560 in ascending order is 0456 and in decending order is 6540.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat the process.

This process will always reach the number 6174 within 7 iterations. Once 6174 is reached the process will continue yielding 6174 because:

• When you arange the digits in 6174 in ascending order you get 1467.
• When you arange the digits in 6174 in decending order you get 7641.
• Subtract 1467 from 7641 and you are back to 6174 (Kaprekar's Constant).

For example, take 4906:

• When you arange the digits in 4906 in ascending order you get 0469.
• When you arange the digits in 4906 in decending order you get 9640.
• Subtract 0469 from 9640 and you get 9171.
• When you arange the digits in 9171 in ascending order you get 1179.
• When you arange the digits in 9171 in decending order you get 9711.
• Subtract 1179 from 9711 and you get 8532.
• When you arange the digits in 8532 in ascending order you get 2358.
• When you arange the digits in 8532 in decending order you get 8532 (no change, the digits are already in decending order).
• Subtract 2358 from 8532 and you get 6174 (Kaprekar's Constant).