Premier League Predictor: FastAPI & Redis — Chapter 8, Exercise 3
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TASK
Compute the guest average in hundredths and in sixtieths for guest sets
scoring [10,40,0], [40,10,10,0,0] and seven guests [10,0,0,0,0,0,0].
Report the rounding error of each, and explain why the sixtieths scheme
stops working at seven guests.

SOLUTION

  [10, 40, 0]             exact 50/3
      hundredths: round(1666.67) = 1667   error 0.3333 hundredths (0.0033 points)
      sixtieths:  50*60/3 = 1000          exact (an integer)

  [40, 10, 10, 0, 0]      exact 12
      hundredths: 1200                    exact
      sixtieths:  60*60/5 = 720           exact

  [10, 0, 0, 0, 0, 0, 0]  exact 10/7
      hundredths: round(142.857) = 143    error 0.1429 hundredths
      sixtieths:  10*60/7 = 600/7 = 85.71...   NOT an integer

Why it stops at seven: every prediction is worth 0, 10 or 40, so the sum
of guest points is a multiple of 10. Multiplying by 60 makes it a multiple
of 600. An integer average needs 600 to divide evenly by the number of
guests. 600 is divisible by 1, 2, 3, 4, 5 and 6, but not by 7. Checked on
200 random cases for each guest count from 1 to 6: always a whole number.
The scheme is exact for a week with up to six guests, and not beyond.

For any guest count, a common denominator would be needed (for example
420 covers 1 to 7), at the cost of a larger integer. Otherwise a rare
seven-guest week still gets a rounding error, as hundredths always do.

WHY THIS WORKS AS AN ANSWER
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It works the three cases with the real arithmetic, explains the limit
from the actual divisibility argument, and states exactly where the
sixtieths scheme is and is not safe.