

From: Nick Baxter 
Sent: Friday, July 31, 2015 6:22 PM
To: Oskar van Deventer 
Subject: Shift Happens

Oskar,
Should I return the two Shift Happens puzzle to you, or give them to Bram?


I don't know if I told you "my" solution to Shift Happens. The analysis was quite interesting.

1. Same as you: solve the 10, 16, 18 gears
2. Count the number of teeth to turn the 20,18,15 gears clockwise so that they would be solved. Call these values x,y,z.
3. Full clockwise turns for 10: (-3x/2 + 2z) mod 6
You could turn counter-clockwise for negative mod values, if desired.
4. Full clockwise turns for 16: (3x/2 - 5y/2) mod 15
5. Full clockwise turns for 18: (5y/2 - 2z) mod 10

Nicely deterministic, and virtually optimal.

Nick

