Choose any 4 digits, possibly with repeats.

Arrange them largest down to smallest (descending order).

Reverse this.

Subtract.

Keep doing this, until you have a good reason to stop

(i.e. not exhaustion or boredom - this is a fairly tedious task to do entirely without a calculator...).

Note that if you obtain just 3 digits e.g. the reverse of 8820 is 0288.

Students could build up some form of overview of what happens for a series of 4 digit numbers (this diagram is a subset of the options). There is a fuller picture on Wiki.

It should take at most 7 iterations (steps) to arrive at Kaprekar's 4-digit constant: 6174 (or 7641 etc)

Students could work with 3-digit numbers instead. This time the 'constant' is 954.

Which 3-digit number takes most steps to reach this?

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