Blocking probabilities calculated by the exact and approximate solutions for various levels of neighbour- spoofed spam calls. The blue curves depict the toy enumeration example above (solid line is exact, dashed line is approximate), for which 𝑛 = 𝟣𝟣 and 𝑘 = 𝟦𝟪. All other curves apply to the number blocking problem, for which 𝑛 = 𝟩𝟩. For these, the exact and approximate results are visually indistinguishable.

Madeleine Hall is a mathematical consultant at the Smith Institute, based in Oxford. She likes writing, open water swimming, the Oxford comma, and tHiS mEmE. Her PhD research was on optimal swimming for microorganisms. She has found none of her results of any use in the lido.

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