Polarium Advance is designed to be played every day. Not just "for as long as it's fun"; every day. The idea is to stick it in your GBA cartridge slot and turn it on every so often. Every day is filled with dead time; Polarium Advance's goal is to fill it. It's the Times crossword. It's a Sudoku puzzle. It's picking at the flap of your shoe. It's concentration and deduction rather than instinct, persistence or digital agility.
The main mode, Daily Polarium, is 365 puzzles. You set today's date and then get going. Completed puzzles unlock more of the calendar. Each puzzle is about making horizontal lines of matching tiles. You do this by snaking a line over the top of them using the d-pad, occasionally overflowing into the margin if you need to, and then hitting A to change the colour of the tiles you've selected from black to white or white to black. If you clear the grid, you solve the puzzle. If you don't, you try again.
When you're done, you're given a rating based on whether you met the two puzzle conditions - to complete it within a certain number of steps (i.e. covering a certain number of squares), and to start and stop in certain places. The specifics of the two conditions are unknown to you the first time you attempt a puzzle, but are revealed on a subsequent visit. As such, even an easy puzzle can become a bit of a challenge as you carefully weigh up which way to move, and triumph can turn bitter in an A-button instant when you realise you've used the right number of steps and started and ended in the right place, but still have an errant white tile in a line of blacks.