PARALLEL (SIMON SINGH): Kaprekar constant

This is a video from the hugely successful maths video channel Numberphile. The channel has received over 300 million views, so I would encourage you to explore some of its other videos if you want to learn more about maths.

Professor Roger Bowley from the University of Nottingham explains why 6,174 is such a special number. Watch it and answer the questions below.

In short:

• Pick any 4 digit number (as long as the digits are not ALL the same).

• Put the digits in ascending order and descending order to create two numbers.

• Subtract the small number from the big number, to create a next stage number.

• Then repeat the process with the new number

• Eventually you end up with 6,174.

  1. Start with the number 4,321. Reverse the digits, take the small number from the big number and what is the result? Clue: it is between 3,000 and 4,000.

  2. Repeat the process, starting with your previous answer – remember to rearrange the digits into ascending order and descending order before subtracting the smaller number from the larger number. What is the result? Clue: it is between 8,000 and 9,000.

  3. Repeat the process, starting with your previous answer – remember to rearrange the digits into ascending order and descending order before subtracting the smaller number from the larger number. What is the result?

  4. Every 4-digit number ends up as 6,174 if we follow the instructions above, but some numbers take longer to get there than others. How many stages does it take for 5,200?

  Clue: To get you started, after the first stage we reach 5,200 – 0025 = 5,175.

Parallel link - Week 1: Wizard of Oz