Let's start with a game.
Think of a positive number (say n).
If it is even then replace it with it's half (n/2).
If it's odd then replace it with three times of itself plus one (3n+1).
for e.g., let's take 15.
since its odd, so it becomes 15*3+1 i.e., 46
now 46 changes to 46/2 i.e., 23
agin 23 changes to 23*3+1 i.e., 70
continuing this we get a sereis.... 15,46,23,70,35,106,53,160,80,40,20,10,5,16,8,4,2,1.....--->
so this continues.
You would be thinking, this is not hard.....Beacause it's not the problem.
The problem is that if you start with any of the positive number eventually it ends up with 1.
Try with some numbers like
11 - 11,34,17,52,26,13,40,20,10,5,16,8,4,2,1
7 - 7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1
13 - 13,40,20,10,5,16,8,4,2,1
This problem drives mathematicians crazy because there don't seems to be any clear pattern.
There are certain amazing numbers like 8192 that collapse down to 1 very quickly i.e in only 13 steps, whereas 27 collapses to 1 after a long time i.e., it takes 112 steps.
OOOOPS!! isn't it amazing.
This impossible problem is called 3n+1 problem.
for more info go to
wikipedia - https://en.wikipedia.org/wiki/Collatz_conjecture
youtube - https://www.youtube.com/watch?v=m4CjXk_b8zo
collatz calculator - http://www.nitrxgen.net/collatz/13/
Think of a positive number (say n).
If it is even then replace it with it's half (n/2).
If it's odd then replace it with three times of itself plus one (3n+1).for e.g., let's take 15.
since its odd, so it becomes 15*3+1 i.e., 46
now 46 changes to 46/2 i.e., 23
agin 23 changes to 23*3+1 i.e., 70
continuing this we get a sereis.... 15,46,23,70,35,106,53,160,80,40,20,10,5,16,8,4,2,1.....--->
so this continues.
You would be thinking, this is not hard.....Beacause it's not the problem.
The problem is that if you start with any of the positive number eventually it ends up with 1.
Try with some numbers like
11 - 11,34,17,52,26,13,40,20,10,5,16,8,4,2,1
7 - 7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1
13 - 13,40,20,10,5,16,8,4,2,1
This problem drives mathematicians crazy because there don't seems to be any clear pattern.There are certain amazing numbers like 8192 that collapse down to 1 very quickly i.e in only 13 steps, whereas 27 collapses to 1 after a long time i.e., it takes 112 steps.
OOOOPS!! isn't it amazing.
This impossible problem is called 3n+1 problem.
for more info go to
wikipedia - https://en.wikipedia.org/wiki/Collatz_conjecture
youtube - https://www.youtube.com/watch?v=m4CjXk_b8zo
collatz calculator - http://www.nitrxgen.net/collatz/13/
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