# Student Projects

## Independent-learning super-curriculum projects: reading, research and ideas shared by Perse students # The Collatz-Sycaruse-Ulam problem: White, P, Year 7

The Collatz-Sycaruse-Ulam problem is when you take a number and then you halve it if it is even and triple it and add 1 if it is odd. The problem is – will every number reach 1? I have made a spreadsheet using the numbers 1 to 100 and they all reach 1 – even 97, which takes 119 steps to get to 1.

The way that I did it was using the IF function to see whether it was odd or even (I used the MOD function to find out that) and if I wanted to find the step after cell Y3, it would have looked like this:

=IF(MOD(Y3,2)=0,Y3/2,Y3*3+1)

This means that if in modulus 2 the number is equal to 0 (which is a long-winded way of saying if the number is even) then halve the number and if it is not equal to 0 then multiply it by 3 and add 1.

I think that every number will reach 1 eventually. For instance, assume that not every number reaches 1. Then where would it get stuck?

To see the spreadsheet click below: