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Re: Collatz Multiple Choice Placement Exam
Posted:
May 4, 2002 9:42 AM
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"William Elliot" <mars@xx.com> wrote in message
news://20020502045557.L86227-100000@agora.rdrop.com...
> Start with a number n and repeat:
> if n is even, then divide it by two
> if n is odd, multiply it by 3 and add 1.
>
> Eventually n will
> 1. reach 1
> 2. get bigger and bigger
> 3. repeat an earlier value
Of course if 3 is true then 1 is untrue (other than the trivial case).
If 2 is true then 1 is untrue.
And conversely if 1 is true both 2 and 3 are untrue.
These three states incidentally match those of the solutions of first order
differential equations -i.e. damping, oscillation and exponential growth.
Or of couse if you like chaos theory there could be a solution which takes
on an infinite set of (chaotic) values - or is this the same as getting
bigger and bigger?
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