Exercise 1: A Small Bucket With a Fast Refill Rate — Possible Solution
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THE SETUP
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    bucket = TokenBucket(capacity=5, refill_rate_per_sec=10)

A smaller bucket (5 tokens) but a much faster refill rate (10/sec)
than this chapter's own original example (10 capacity, 2/sec refill).

RESULTS
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    first 5 immediate requests: [True, True, True, True, True]
    second batch after 0.3s wait: [True, True, True, False, False]
    second batch allowed count: 3
    expected refill: 0.3s * 10/sec = 3 tokens

All 5 immediate requests succeeded, correctly draining the bucket to 0
tokens. After waiting 0.3 seconds, 3 of the next 5 requests succeeded,
and 2 were rejected.

WHY EXACTLY 3, USING THIS CHAPTER'S OWN REFILL FORMULA
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This chapter's own _refill() logic computes
`tokens + elapsed_seconds * refill_rate_per_sec`. With the bucket
starting at 0 tokens after the first batch, and 0.3 seconds elapsing
at a refill rate of 10 tokens/sec: 0.3 * 10 = 3.0 tokens refilled
exactly. The next three allow_request() calls each correctly consume
one of those 3 refilled tokens (succeeding), and the fourth call finds
the bucket back at 0 (rejecting), matching the observed [True, True,
True, False, False] pattern precisely.

WHY THIS CONFIRMS THE REFILL MATH IS EXACT, NOT APPROXIMATE
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This chapter's own original example only verified a qualitative claim
("waiting refills roughly 1 token, allowing one more request"). This
exercise verifies the refill amount PRECISELY predicts the number of
additional successful requests - 0.3 seconds at 10/sec produces
exactly 3 tokens, and exactly 3 (not 2 or 4) requests succeed,
confirming the formula's own elapsed-time * rate calculation is being
applied correctly rather than just roughly in the right direction.

WHY THIS WORKS AS AN ANSWER
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The new bucket parameters are chosen specifically to make the refill
math easy to verify precisely (0.3 * 10 = a clean 3), the actual
result is checked against that exact predicted number rather than a
vague expectation, and the underlying formula is traced through
directly to explain why 3 (not some other number) is the correct
result.