Three tennis paradoxes -- The uphill roller -- The birthday paradox -- The spin of a table -- Derangements -- Conway's chequerboard army -- The toss of a needle -- Torricelli's trumpet -- Nontransitive effects -- A pursuit problem -- Parrondo's games -- Hyperdimensions -- Friday the 13th -- Fractran -- The motifs -- Appendix A: the inclusion-exclusion principle -- Appendix B: the binomial inversion formula -- Appendix C: surface area and arc length.