don steward
mathematics teaching 10 ~ 16

Tuesday, 15 February 2011

Kaprekar's constant

Choose any 4 digits, possibly with repeats.
Arrange them largest down to smallest (descending order).
Reverse this.

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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