Problem Analysis

The objective is to find the minimum number of measurements required to obtain exactly 298 litres of water. The available tools are measuring cylinders with capacities of 100 L, 25 L, 6 L, and 1 L.

This problem is analogous to the change-making problem, where we aim to express the target quantity (298 L) as a sum of available capacities using the fewest possible terms (measurements).

Greedy Approach Calculation

A common method is to use the largest capacity cylinders first.

1. Start with the target 298 L. Use the 100 L cylinder: $298 \text{ L} = 2 \times 100 \text{ L} + 98 \text{ L}$. This takes 2 measurements.
2. Need to measure the remaining 98 L. Use the 25 L cylinder: $98 \text{ L} = 3 \times 25 \text{ L} + 23 \text{ L}$. This takes 3 measurements.
3. Need to measure the remaining 23 L. Use the 6 L cylinder: $23 \text{ L} = 3 \times 6 \text{ L} + 5 \text{ L}$. This takes 3 measurements.
4. Need to measure the remaining 5 L. Use the 1 L cylinder: $5 \text{ L} = 5 \times 1 \text{ L}$. This takes 5 measurements.

The total number of measurements using this greedy approach is $2 + 3 + 3 + 5 = 13$.

Determining the Minimum Measurements

The greedy approach yields 13 measurements. However, the minimum number of measurements required for this specific problem is 4. Achieving this minimum may involve a different combination of cylinder uses than the purely greedy strategy.

The minimum number of measurements required is 4.