Daily Math Puzzle: 2026-05-20
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2026-05-20
In the ancient kingdom of Khar, two construction crews work on a defensive wall. Crew A has 10 workers and can lay 4 meters of wall each day. Crew B has 15 workers and can lay 6 meters of wall each day. The king orders a 100‑meter wall to be finished in exactly 5 days. The crews may reassign any number of workers from Crew B to Crew A (or vice‑versa) each day, but a worker can belong to only one crew on a given day. What is the minimum number of workers that must be moved from Crew B to Crew A each day to meet the deadline?
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Solution
It cannot be done — First find the daily work needed: 100 m ÷ 5 days = 20 m per day. Crew A’s per‑worker rate is 4 m ÷ 10 workers = 0.4 m/worker·day. Crew B’s per‑worker rate is 6 m ÷ 15 workers = 0.4 m/worker·day. Both crews have the same productivity per worker. No matter how the 25 workers are divided, the total daily output is 25 workers × 0.4 m/worker·day = 10 m per day. This is only half of the 20 m per day required. Because the overall productivity cannot be increased by moving workers between crews, the wall cannot be completed in the allotted time. Therefore the correct answer is that it cannot be done.
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