At the end of the school day, Michael goes to the bike rack, but discovers that someone has placed a lock on his bike. A note on the bike reads:
Sorry for locking your bike, but the combination is 1/2/3/4!
The lock has four dials, each with the digits 0 to 9. However, to Michael's surprise, he discovers that turning the first dial moves the second dial the same amount. After a little experimentation, he realizes that each dial is connected to its immediate neighbors, and moving any dial causes those neighbors to move the same amount. The dials are circular, so that the digit after 9 is 0, and the digit before 0 is 9.
Now Mike is worried that he may be stuck at the bike rack for a long time!
Puzzle 1: When Mike found his bike locked, the combination on the lock displayed 1/4/9/2. Is it possible to turn the dials to the 1/2/3/4 combination and unlock the bike?
Puzzle 2: Is it possible to reach 1/2/3/4 no matter what the starting combination is? Can you get from any starting combination to any legal final combination?
Thanks to Logan Burkardt for discovering this puzzle!
I give up, show me the solution.