Balancing Cards

Take a full suit of 13 cards. Each card weighs as many ounces as its value. Aces weigh 1 ounce, Jacks weigh 11, Queens weigh 12, and Kings weigh 13 ounces. Take four bars of length 4 inches and create a mobile with the cards. You can tie to each bar in 5 places (at locations 0, 1, 2, 3, and 4 inches.) You can only tie once to each location. On the lowest bar, tie 4 cards, and one string up to the next bar. On the other three bars, tie 3 cards, one string down to the previous bar, and one string up to the next (the top bar has one string up to the ceiling.) All bars balance. Assume the weight of the bars and strings are negligible. Try to find solutions for which the center of mass is as high as possible and as low as possible.

Source: Original.

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