The article presents two challenging puzzles: identifying the lowest and highest cards among 100 without turning them, and safely descending a 20m building using a rope. In the card puzzle, the goal is to reduce the number of comparisons required to find the 1 and 100 cards efficiently. Instead of making 198 comparisons, a more optimal strategy is discussed. The second puzzle involves a burglar with a 15m rope at the top of a building, where using creative knotting techniques can facilitate a safe descent onto a ledge and ultimately to the ground.
To identify both the 1 and 100 cards, you can use a more efficient strategy that involves pairing cards and intelligently selecting which to compare next.
The key insight lies in reducing redundancy: instead of 198 comparisons, you can progressively eliminate possibilities, leading to identifying both extreme cards with fewer total comparisons.
The burglar's strategy involves using the 15m rope creatively: secure one end to the hook at the top, and let the rope hang down to reach the ledge.
By tying a knot in the rope at the 5m mark, the burglar can safely lower themselves to the ledge, then use the remaining rope to descend.
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