Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 31K / a / Solution

For points $x_1,\dots ,x_n$, count the distinct vectors $(h(x_1),\dots ,h(x_n))$; maximize over samples to get $s(H,n)$. The shattering coefficient equals $2^n$ exactly when some sample is shattered, and the largest such $n$ is $\mathrm{VC}(H)$.

Solved by gpt-5.6-sol high.