Produced by Stephen Schulze, Jonathan Ingram and the Online Distributed Proofreading Team at https://www.pgdp.net [Transcribers note: Many of the puzzles in this book assume a familiarity with the currency of Great Britain in the early 1900s. As this is likely not common knowledge for those outside Britain (and possibly many within,) I am including a chart of relative values. The most common units used were: the Penny, abbreviated: d. (from the Roman penny, denarius) the Shilling, abbreviated: s. the Pound, abbreviated: L There was 12 Pennies to a Shilling and 20 Shillings to a Pound, so there was 240 Pennies in a Pound. To further complicate things, there were many coins which were various fractional values of Pennies, Shillings or Pounds. Farthing 1/4d. Half-penny 1/2d. Penny 1d. Three-penny 3d. Sixpence (or tanner) 6d. Shilling (or bob) 1s. Florin or two shilling piece 2s. Half-crown (or half-dollar) 2s. 6d. Double-florin 4s. Crown (or dollar) 5s. Half-Sovereign 10s. Sovereign (or Pound) L1 or 20s. This is by no means a comprehensive list, but it should be adequate to solve the puzzles in this book. Exponents are represented in this text by ^, e.g. '3 squared' is 3^2. Numbers with fractional components (other than 1/4, 1/2 and 3/4) have a + symbol separating the whole number component from the fraction. It makes the fraction look odd, but yeilds correct solutions no matter how it is interpreted. E.G., 4 and eleven twenty-thirds is 4+11/23, not 411/23 or 4-11/23. ] AMUSEMENTS IN MATHEMATICS by HENRY ERNEST DUDENEY In Mathematicks he was greater Than Tycho Brahe or Erra Pater: For he, by geometrick scale, Could take the size of pots of ale; Resolve, by sines and tangents, straight, If bread or butter wanted weight; And wisely tell what hour o' th' day The clock does strike by algebra. BUTLER'S _Hudibras_. 1917 PREFACE In issuing this volume of my Mathematical Puzzles, of which some have appeared in periodicals and others are given here for the first time, I must acknowledge the encouragement that I have received from many unknown correspondents, at home and abroad, who have expressed a desire to have the problems in a collected form, with some of the solutions given at greater length than is possible in magazines and newspapers. Though I have included a few old puzzles that have interested the world for generations, where I felt that there was something new to be said about them, the problems are in the main original. It is true that some of these have become widely known through the press, and it is possible that the reader may be glad to know their source.