To get back to where it started, the disk must have   
rotated through a multiple of 360°, and also through a 
multiple of 150°.  We find the least common multiple 
of 150° and 360°

150 = 2∙3∙5²
360 = 2³∙3²∙5

The least common multiple needs
2 as a factor 3 times, 3 as a
factor 2 times, and 5 as a factor
2 times.

So the LCM is 2³∙3²∙5² = 1800°

That means the 150° has been added
1800°/150° = 12 times.

Since we started before noon on a 
Saturday, it rotated the first 150°
at noon on Saturday. Heck, let's just
go through the 12 days day by day until the
disk has rotated through 1800° and see what 
day we end up on:

1. Saturday noon it had rotated through 150°
2. Sunday noon it had rotated through 300°
3. Monday noon it had rotated through 450°
4. Tuesday noon it had rotated through 600°
5. Wednesday noon it had rotated through 750°
6. Thursday noon it had rotated through 900°
7. Friday noon it had rotated through 1050°
8. Saturday noon it had rotated through 1200°
9. Sunday noon it had rotated through 1350°
10. Monday noon it had rotated through 1500°
11. Tuesday noon it had rotated through 1650°
12. Wednesday noon it had rotated through 1800°, 
which is the first time it had rotated through 
a multiple of 360°

Edwin