Discussion

How many odd days are there in 100 years ?

Answer: C

Correct answer: 5

In 100 years there are 24 leap years and 76 ordinary years, since 1900-style century years are not leap.

\[\text{Odd days} = 76 \times 1 + 24 \times 2 = 76 + 48 = 124\]

\[124 = 17 \times 7 + 5\]

So 100 years carry 5 odd days, which is why 200 years carry 3, 300 carry 1 and 400 carry none.

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