# Today Puzzle #589 ## Puzzle No. 589 – Tuesday 15 October

I use an amazing four digit PIN for everything, but I never write it down because I can always calculate it. Simply choose any four digit number to start and re-arrange the digits to create the largest and also the smallest possible numbers. Subtract the smallest from the largest to produce another four digit number and simply repeat no more than eight times until my PIN is repeated and thus revealed.

Today’s #PuzzleForToday has been set by Maths' Department at Royal Hospital School in Suffolk

The magic PIN number will always be 6174, whatever numbers you choose, and is known as Kapreka's Constant, named after the Indian mathematician, D R Kapreka, who discovered this in 1949.

When the process is followed for any four digit number, it always ends up with 6174.

If you started with 6174, 7641-1467 = 6174 which then repeats forever.

However, let's say you started with the year that the Royal Hospital School was founded - 1712

7211-1127 = 6084; 8640-0468= 8172; 8721-1278 =7443; 7443-3447= 3996; 9963-3699 = 6264; 6642-2466 = 4176; 7641-1467 = 6174

This works for every four digit number, although you must retain leading zeros as follows

2111 -1112 = 0999 (and not 999); 9990-0999 = 8991; 9981-1899 = 8082; 8820-0288 =8532; 8532-2358 = 6174  