What is the minimum number of times one needs to measure to get $298$ litres of water from a tank, if the measuring cylinders have capacities $1$ litre, $6$ litres, $25$ litres and $100$ litres?
Detailed Explanation:
Target = 298 litres. Optimal strategy: overshoot using large cylinders, then subtract excess.
Draw 3 × 100 = 300 litres (3 measurements). Excess = 300 − 298 = 2 litres. Pour back 2 × 1 litre = 2 litres (2 measurements). Total = 3 + 2 = 5 measurements.
Greedy approach (only adding) needs 13 measurements: 2×100 + 3×25 + 3×6 + 5×1. Using 4 measurements yields 299 or 294 litres, not exactly 298.
Therefore, the minimum is 5 measurements, making Option 2 the correct answer.
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