## Tuesday, February 18, 2014

### Review: Clock Day for iPhone and iPad

Clock Day by Morningtea Studios is an interesting and fun way to present something that math students might otherwise find repetitive and boring.
It doesn't look like a math puzzle from the title screen, does it? Indeed it seems colorful and inoffensive. But what's behind the facade can get quite tricky.

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.
Now to solve this kind of puzzles you can just random tinker with the clocks until you get it, or you can think a little more about it and figure out the exact steps you need. Or, you can realize that this is nothing else that a representation of a system of equations using modular arithmetic.

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.
A sleepy clock, which can't be moved directly but only awakened or put to sleep again. The arrows affect it only while it's awake.
A spinning clock which can be moved directly only in one direction; use the arrows to make it change direction.
A lazy clock (a bit sexistly depicted with a female face) which doesn't move directly and can only be moved using the arrows.
My favorite so far: a clock which propagates the commands received from the arrows. So in this example moving the top left clock will move the bottom clock which in turn will move the top right clock.
Kudos to the designer: it must not have been easy to come up with the ideas for the 11 different clocks included in the game.

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 :-)

### Summary

 Nontrivialness ★★★☆☆ Logical Reasoning ★★★★☆ User Interface ★★★★☆ Presentation ★★★★☆ Loading Time ★★★★★ Saves Partial Progress ✘ Status Bar ✔

©2014 Nicola Salmoria. Unauthorized use and/or duplication without express and written permission is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Nicola Salmoria and nontrivialgames.blogspot.com with appropriate and specific direction to the original content.