Created 11th March, 2010 04:01 (UTC), last edited 11th March, 2010 05:21 (UTC)

Collatz

We've done a variation on this puzzle before, but then of course there wasn't a cool XKCD comic.

The sequence can be defined in this way:

n -> n/2 (n is even) n -> 3n + 1 (n is odd)

And the conjecture is that no matter what positive starting integer you start from the sequence of numbers will always reach one. I.e., starting from 13 gives the following sequence:

13 40 20 10 5 16 8 4 2 1

For odd numbers we do the following: 3*n* + 1, where *n* is the current integer in the sequence. Is the three arbitrary, or does the conjecture not work for other odd values? I.e. if we take the formula as *k*.*n* + 1 does every positive integer still eventually reduce to 1?

**Write a program that checks to see if the conjecture holds for k = 5**

Three and five are just two values of course.

**Check to see if the conjecture holds for other odd values of k**

How far can you check? What bounds are you putting on the calculations? And, how many of your friends have called whilst you've been doing it?

Categories: BeerCamp puzzle ● Mathematics

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