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Stupid number trick IV (Posted on 2006-01-13) Difficulty: 3 of 5
Take any whole number greater than one.

1. If the number is odd, multiply it by three and add one.
2. If it is even divide it by two.
2a. If the result is still even, continue to divide by two until the result is odd.
3. Continue steps 1 and 2 until you get the same number twice.

[For example starting with 9 -> 28 -> 14 -> 7 which is considered one iteration. The next iteration brings this to 11.]

What number(s) does this process terminate at?
What starting value less than 200 takes the most iterations to terminate?

  Submitted by Jer    
Rating: 4.0000 (4 votes)
Solution: (Hide)
It is pretty clear (although unproven) that the process always terminates. The process terminates at 1.

The number less than 200 requiring the most steps is 171 which takes 45.

See Justin's posts for larger numbers taking more steps.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: any suggestions?Hugo2006-02-04 14:53:31
any suggestions?Justin2006-02-03 23:11:23
*sniff*Hugo2006-02-03 21:05:03
Some Thoughts*sniff* (20 billion and no further) (starts crying)Justin2006-02-03 19:05:00
Some Thoughts14 billion and climbingJustin2006-01-24 11:04:28
Some ThoughtsNothing better to do (Up to 1 billion)Justin2006-01-21 14:31:03
Some ThoughtsSick of re(...), but here you goJustin2006-01-20 23:45:57
re(6): Going further (520,000,000+)Justin2006-01-20 13:44:27
Interesting . . . . . . . .Justin2006-01-20 13:41:34
re(5): Going further (520,000,000+)Hugo2006-01-20 13:04:51
re(4): Going further (520,000,000+)Justin2006-01-20 12:58:41
re(3): Going further (520,000,000+)Hugo2006-01-20 12:54:45
re(2): Going further (520,000,000+)Justin2006-01-20 09:05:18
re: Going further (520,000,000+)Hugo2006-01-19 17:24:25
Going further (520,000,000+)Justin2006-01-19 14:01:40
Questionre: AnswerJustin2006-01-19 13:49:01
re: Collatz ConjecturegoFish2006-01-14 02:20:05
AnswerJoe2006-01-13 20:18:47
Hints/TipsCollatz ConjectureThe riddler2006-01-13 19:04:03
A ContributiongoFish2006-01-13 18:52:17
re: interesting propertypcbouhid2006-01-13 16:11:34
interesting propertyBob Smith2006-01-13 15:36:31
TerminationDan2006-01-13 15:33:28
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