Ziay!

matttlocke

busy work, for those of you who like math, can you fgure out if there is a number which does not go down to 1 given the following

if the number is even apply the following : n/2
if the number is odd apply the following : 3n + 1

ex 5
3(5) + 1 = 16
16/2 + 8
8/2 = 4
4/2 = 2
2/2 = 1
3(1) +1 = 4
4/2 = 2
2/2 = 1
repeats...
in addition, what would be some ways that a number would not necessarily go down to 1
numbers should be positive
to clarify further, the numbers must be integers, positive, and not zero
I really like the VB code, and thats a good approach because you can try lots of numbers quickly, however the size of teh numbers is limited,you probably wan tto look at extremely large numbers
Yes this is also known as teh collatz problem (spelled something like that), i deliberately didnt give that piece of information, plus i did state it was busy work, i suspect that at a large enough number there will ultimately be a repeating pattern

Philip N

There are no numbers that will work. Any odd number multiplied by 3 will make an odd answer. Plus 1 makes it even and all even numbers will divide down to 1.

darKnight

I don't remember what we said the answer was. I think we said no they all go down to 1.

aditsu

If anybody could answer your question, they would not answer it here but publish it and collect the money and FAME!

So far, the greatest mathematicians in the world have been utterly defeated by this problem. Did you really expect someone would solve it here?

mypublicident

-1 works
-1*3 + 1 = -2
-2/2 = -1 (back to where we started)

Addition> Now you say they should be pos! Jeez

0 works though is it technically positive?

Wow, try a number like .1 - The numbers get REALLY big before coming back down to 1. (5.00315450989997E+15)


Function IsOddNum(ByVal intNumber As Double) As Boolean
If (intNumber Mod 2 = 0) Then
Return False
Else
Return True
End If
End Function

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Dim num As Double = Convert.ToDouble(TextBox1.Text)
Dim count As Integer = 0
Literal1.Text = num.ToString() & "<BR>"
While num <> 1 And count <> 1000
If IsOddNum(num) Then
num = 3 * num + 1
Else
num = num / 2
End If
Literal1.Text &= num.ToString() & "<BR>"
count += 1
End While
End Sub


Another Note: I just plotted the number of iterations for the numbers between 1 and 20,000. The graph totally shows a pattern! (Mathematicians love patterns)

Another Note, Doh, now the numbers have to be integers? Jeez, there goes my repeating number answer. Are you going to keep adding rules every time I get it right? LOL