The basic idea is simple: you have some clocks, which are connected by arrows. You can change the time shown by each clock, one hour at a time, but when you adjust one clock the movement will propagate to the other ones through the arrows. So for example, in the puzzle below, if you advance the clock on the top right by 1 hour, the one at the bottom will also advance by 1 hour, and the one on the top left will advance by 2 hours (because the arrow has a 2 on it).
The goal is to bring all clocks to 12 o'clock at the same time.
For example, for the puzzle above the system would be:
x + 2y = 5 (mod 12)
x + y = 3 (mod 12)
y + z = 2 (mod 12)
you can solve it using your preferred method to find
x = 1
y = 2
z = 0
so advance the top left clock by 1 hour, advance the top right one by 2 hours. Done!
Clock Day has 120 puzzles (15 are free, the rest can be unlocked with a single in-app purchase). The nice thing about it is that it continues to introduce new mechanics, in the form of new clock characters, throughout the game, so the puzzles remain fresh. Here are the first ones I found.
A crazy clock, which moves backwards when affected by an arrow. This maps to minus signs in the equations.
I liked the puzzles, but the interactions between the clocks can be quite complicated and confusing. It sometimes was hard to find the solution without sitting down and converting the puzzle to a proper system of equations. This was more of a problem in some of the first few puzzles, where I thought that the difficulty curve hadn't been carefully balanced. For example, I think it would have made sense to introduce the Lazy clock at the beginning, because it makes the puzzles easier since it only affects other clocks and not itself.
Other minor flaws are lack of Game Center integration for the game's achievements, and a somewhat annoying short music loop (I just played with sound off).
Other than that, the game is pretty good and since it's free it's worth taking a look at.
I think this could be an excellent way to teach students how to formalize a problem into a system of equations. Solving the system and plugging the results into the game to see them work first time should be a particularly rewarding feeling and reinforce faith in the power and usefulness of mathematics :-)
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