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Jishaku is a new game that combines magnets with egg-crate foam to create a simple strategy game that relies on both logical placement of pieces and an understanding of magnetism and polarity; not exactly a high-strategy game, but one that does reward both logical play and dexterity, and has more nuance than you might think - piece selection is key when you get into tight spots (some of the magnets are smaller than others, and even their shapes are a factor). We had a blast playing this both between adults and with our nearly four-year-old. A slightly older child might actually even try NOT to pick up the magnets on every turn. $20 on Amazon.com.
A brief video, after the jump.
https://www.youtube.com/watch?v=OnuMFjsFZWA