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