Solutions for the puzzles. The rest of the achievements are for failing a puzzle in each Age and attempting to play both madness levels.
Age 1
Age 1 easy:
Turn the gears in this order: 3 1 2
Age 1 advanced:
Turn the arrows: left right right left right. They should look like this:
Then turn the gears in this order: 3 1 2 4 5
Age 1 hard:
Change the gems to these colors: black, gold/orange, purple, red, white/peach, silver. They should look like this:
Then turn the gears in this order: 3 4 1 2 6 5
Age 3
Age 3 easy:
Turn the gears in this order: 2 1 3
Age 3 advanced:
Turn the arrows: left right right left right. They should look like this:
Then turn the gears in this order: 2 3 1 5 4
Age 3 hard:
Change the colors to: brown, pink, purple, green, orange, gray. They should look like this:
Then turn the gears in this order: 3 4 6 5 1 2