This game is available late at night. Enter your house at exactly 12:00 am. The time in the corner of your screen should read "0:00 am". Walk up to your TV and press the A button to play the Bear Shuffle.
The Witch Princess will appear on your screen, along with 3 Da-chan bears. She will sprinkle colored powder (red, yellow, and blue) on the bears and then shuffle them around. You then have to pick the bear that holds the powder she requests. This game plays just like Won's Apple Game from More Friends Of Mineral Town. The more rounds you win, the faster Witch shuffles the bears around. If you get the answer wrong, the game ends.
The game lasts 10 rounds. After you have passed the last one the game will be over. Unfortunately you don't win any prizes for this game, but you will earn 100 LP with the Witch Princess.
An easy way to win this game is to pause it by pressing the start button while the Witch Princess is shuffling the bears. This way it is easier to see which bears are going where.