a) There are two ropes. If either of them is lit at one end, it will burn for an hour. The ropes burn unevenly. For example, it cannot be guaranteed that half of the rope will burn in 30 minutes. How can you measure a 15-minute interval using two such ropes?

b) How many time intervals (including the zeroth) can be measured using three such ropes?
| a) The first rope should be lit from both ends, and the second one from one end. After the first rope burns out, the second one will have 30 minutes left to burn. To halve this interval, the second end of the remaining rope should also be lit.

b) $2^{4}-1$.

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