Kaprekar's Constant

Goals

1. Finding patterns in numbers

2. Practicing 3 and 4 digit subtraction

What To Do

• 1. First Explain the Process

     1. Pick a 3 digit number, e.g. 268

     2. Write the biggest number you can make with these digits, e.g. 862

     3. Write the smallest number you can write with these digits, e.g. 268

     4. Subtract the smaller number from the bigger number

     5. Repeat steps 1.2-1.4.

  2. Get each kid to pick their own 3 digit number and follow the steps described above

  3. Ask them to repeat the process at least 4 times

  4. Make a chart and write up all the results from each kid's number

  5. Review the chart and get the kids to look for patterns

  6. Repeat the steps 2-4 if necessary

Additional Work

Try the same process with a 4 digit number and even a 5 digit number. Note the results may not be the same in all these cases.

Background Information

• • Kaprekar's Constant - Wikipedia

  • Kaprekar's Constant - Numberphile Video