B - Bowling Editorial by rng58_admin


Again, the solution is very simple, but it may be hard to come up with.

Let \(\vec{p}, \vec{q}, \vec{r}\) be vectors of random lengths that are parallel to A, B, and C’s viewing directions. Then, the set

\(\{ i \vec{p} + j \vec{q} + k \vec{r} \ | \ 0 \leq i, j, k < 10 \}\)

satisfies the conditions.

Why? For example, from A’s direction, only the values of \(j\) and \(k\) matter, and A can see only \(100\) points. However, D sees all \(1000\) points.

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