114.--_The Tramps and the Biscuits._ The smallest number of biscuits must have been 1021, from which it is evident that they were of that miniature description that finds favour in the nursery. The general solution is that for _n_ men the number must be _m_ (_n_^{_n_+1}) - (_n_ - 1), where _m_ is any integer. Each man will receive _m_ (_n_ - 1)^_n_ - 1 biscuits at the final division, though in the case of two men, when _m_ = 1, the final distribution only benefits the dog. Of course, in every case each man steals an _n_th of the number of biscuits, after giving the odd one to the dog. INDEX "Abracadabra," 64. Age and Kinship Puzzles, 20, 28. Albanna, Ibn, 198. Ale, Measuring the, 29. Algebraical Puzzles. See Arithmetical Puzzles. Alkalaçadi, 198. Amulet, The, 64, 190. Archery Butt, The, 60, 187. Arithmetical Puzzles, 18, 26, 34, 36, 45, 46, 51, 56, 59, 61, 64, 65, 73, 74, 75, 88, 89, 91, 92, 103, 107, 122, 125, 128, 129, 130, 135, 137, 139, 143, 147, 148, 150, 151, 152, 153, 154, 157, 158, 161. Arrows, The Nine, 32. Astronomical Problem, 55. Bags, Four Money, 46. Ball, W. W. Rouse, 202. Bandy-Ball, The Game of, 58, 185. Bears, Capt. Longbow and the, 132, 233. Bergholt, Ernest, 237. Bewley, E. D., 237. Biscuits, The Tramps and the, 160, 250. Block, Cutting a Wood, 160, 250. Blocks, The Number, 139, 238. Bottles, Sharing the, 122. Bottles, The Sixteen, 45. Bridges, The Eight, 48. Bridging the Ditch, 83, 204. Brooch, Cutting the, 41. Buried Treasure, 107, 212. Buttons and String Method, 171, 239. Canon's Yeoman, Puzzle of the, 55, 181. Canterbury Pilgrim's Puzzle, 33. Canterbury Puzzles, 23, 163. Card Puzzle, 125. Carpenter's Puzzle, The, 31, 168. Carpet, Japanese Ladies and, 131, 231. Carroll, Lewis, 246. Casket, Lady Isabel's, 67, 191. Cats and Mice, 75. Cellarer, The Riddle of the, 73, 196. Cellarman, The Perplexed, 122, 222. Chalked Numbers, The, 89, 206. Chaucer's Puzzle, 54, 181. Cheeses on Stools, 24. Chessboard Problems, 21, 25, 32, 51, 72, 82, 90, 113, 114, 116, 119, 124, 138, 141. Chessboard, The Broken, 119, 220. Chifu-Chemulpo Puzzle, 134, 235. Chinese Railways, The, 127, 224. Christmas Puzzle Party, The Squire's, 86, 205. Cisterns, Making, 145. Clerk of Oxenford's Puzzle, The, 29, 167. Cliff Mystery, The Cornish, 99, 210. Clock Puzzle, 158. Cloth, Cutting the, 50. Clowns, The Eight, 128, 226. Club, Adventures of the Puzzle, 94, 210. Coinage Puzzle, The, 111, 214. Coin Magic Square, 111. Column, The Nelson, 146, 241. Combination and Group Problems, 38, 39, 61, 70, 122, 137, 147. Cook's Puzzle, The, 36, 171. Cornish Cliff Mystery, The, 99, 210. Counter Problems, Moving, 24, 35, 69, 77, 124, 135, 136, 141. Counting out Puzzle, 39. Crescent and the Cross, The, 63, 189. Crossing River Problems, 82, 83.