 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/discrete-mathematics-probability-and-continuous-mathematics/1/d/iii/solution

The floor function is constant at

j

on the four consecutive integers

4 j, 4 j + 1, 4 j + 2, 4 j + 3

. Consequently the partition of a set is ${{4 j, 4 j + 1, 4 j + 2, 4 j + 3} : j \in N}$ . Different blocks are disjoint and every nonnegative integer has exactly one quotient and remainder upon division by

4

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