Kaprekar's Constant

Dattaraya Ramchandra Kaprekar (1905–1986) was an Indian recreational mathematician who described several classes of natural numbers including the Kaprekar, Harshad and Self numbers and discovered the Kaprekar Constant, named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well known in recreational mathematics circles Ex Wikipedia.

 
 

• Ask your students to choose any four digit number

1. Now using the digits write the largest four digit number

2. Using the digits write the smallest four digit number

3. Subtract the smallest four digit number from the larger

4. Use the answer, just found, and repeat steps 2 and 3 until an interesting situation arrives

 2376

             7632

            -2367 

5265(one step)

             6552

            -2556

3996(two steps)

             9963

            -3699

6264(three steps)

etc

 
• Investigate:
Which four digit numbers have the greatest number of steps to arrive at the situation found in 4 above?  (This is best as a whole class activity, with Butcher's Paper displaying 1 step, 2 step, 3 step etc students add their starting number on the appropriate sheet)

Which four digit numbers have the smallest number of steps to arrive at the situation found in 4 above?

Are there any four digit numbers which do not stop?

What happens if you start with a 3 digit number and follow the above steps?

Is there a similar situation with five digit numbers? 

Report:
Present a report to your class explaining what you have found justifying your results. A class report could be published in the School Newspaper