Premier League Predictor: FastAPI & Redis — Chapter 7, Exercise 2
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TASK
Compute the composite score by hand for two teams that collide when goal
difference reaches +500 (3 points versus 4 points at -500) and when goals
scored reaches 1,000. Report the real numbers, then propose a wider
packing that removes both collisions and state what its new limits are.

SOLUTION

Chapter packing: points*1_000_000 + (gd+500)*1_000 + gf

  A: 3 points, GD +500, GF 0    = 3_000_000 + 1000*1000 + 0 = 4000000
  B: 4 points, GD -500, GF 0    = 4_000_000 +    0*1000 + 0 = 4000000
  -> identical, so the table treats them as tied

  A: 3 points, GD 0, GF 1000    = 3_000_000 + 500*1000 + 1000 = 3501000
  B: 3 points, GD +1, GF 0      = 3_000_000 + 501*1000 +    0 = 3501000
  -> identical

In both cases one field's value has reached the size of the field above
it and carries into it.

Wider packing:

  composite = points*10**12 + (gd + 10**4)*10**6 + gf

  A (3 points, GD +500, GF 0)   = 3010500000000
  B (4 points, GD -500, GF 0)   = 4009500000000      different
  A (3 points, GD 0, GF 1000)   = 3010000001000
  B (3 points, GD +1, GF 0)     = 3010001000000      different

New limits: goal difference within +/-9,999; goals scored below
1,000,000; points bounded only by the total below.

The largest realistic composite (114 points, GD +100, GF 120) is
114010100000120, about 1.1e14, well below 2**53 = 9007199254740992, so the
double that stores the score still holds it exactly.

The real ceiling is 2**53: past it, a double cannot represent every
integer, and two different composites could round to the same score.
Widening the packing moves the collision limits out but must stay
under that ceiling.

WHY THIS WORKS AS AN ANSWER
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It shows the collision with the actual numbers, explains it as carry
between packed fields, and checks the fix against both the collisions
and the 2**53 exactness limit rather than only widening the fields.