 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability/discrete-mathematics/1/c/ii/solution

Let

A_{d}

contain the multiples of

d

among

1, \dots, 999

⌊ 999/ d ⌋

, using the floor function. Because

3, 7, 11

are pairwise coprime, their pairwise intersections correspond to divisibility by

21, 33, 77

, and their triple intersection to divisibility by

231

333 + 142 + 90 - 47 - 30 - 12 + 4 = 480.

 New to topics? Read the docs here!