Exercise 1: Why free_space() Drops by 16 Bytes, Not 8 — Possible Solution
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THE TEST
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    p = Page()
    initial_free = p.free_space()
    p.add_record(b'12345678')   # 8 bytes
    after_one = p.free_space()

RESULT
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    initial_free -> 60   (PAGE_SIZE=64 minus HEADER_SIZE=4)
    after_one -> 44
    drop: 60 - 44 = 16 bytes

WHY THE DROP IS 16, NOT 8
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free_space() is defined as:

    def free_space(self):
        return self.free_space_end - (HEADER_SIZE + self.num_slots * SLOT_SIZE)

This is the gap between where the slot directory currently ENDS
(HEADER_SIZE + num_slots*SLOT_SIZE) and where the record data
currently BEGINS (free_space_end) -- the genuinely usable middle
region. Adding one 8-byte record changes BOTH sides of that gap at
once:

  1. free_space_end moves DOWN by exactly the record's own length (8
     bytes) -- the record data claims 8 bytes from the data-growing end.
  2. num_slots increases by 1, so HEADER_SIZE + num_slots*SLOT_SIZE
     moves UP by exactly SLOT_SIZE (8 bytes) -- the slot directory
     claims 8 bytes from the slot-growing end.

Since free_space() is the DIFFERENCE between these two boundaries, and
one boundary moved down by 8 while the other moved up by 8, the total
gap shrinks by 8 + 8 = 16 -- both movements eat into the same shared
middle region from opposite directions at once.

WHY THIS WORKS AS AN ANSWER
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This is the direct, numeric confirmation of the chapter's own central
finding: storing ANY record costs the page two separate things, not
one -- the record's own raw bytes, AND a fixed SLOT_SIZE-byte entry in
the slot directory to describe where those bytes are. free_space()
correctly reflects both costs together because it's defined purely in
terms of the two boundaries that each cost individually moves -- there's
no separate "subtract the slot overhead" step bolted on afterward; it
falls out naturally from tracking where the two regions currently sit.