The seventeen whose solutions are practically valueless are ARDMORE, A READY RECKONER, ARTHUR, BOG-LARK, BOG-OAK, BRIDGET, FIRST ATTEMPT, J. L. C., M. E. T., ROSE, ROWENA, SEA-BREEZE, SYLVIA, THISTLEDOWN, THREE-FIFTHS ASLEEP, VENDREDI, and WINIFRED. BOG-LARK tries it by a sort of "rule of false," assuming experimentally that Nos. 1, 2, weigh 6 lbs. each, and having thus produced 17-1/2, instead of 16, as the weight of 1, 3, and 5, she removes "the superfluous pound and a half," but does not explain how she knows from which to take it. THREE-FIFTHS ASLEEP says that (when in that peculiar state) "it seemed perfectly clear" to her that, "3 out of the 5 sacks being weighed twice over, 3/5 of 45 = 27, must be the total weight of the 5 sacks." As to which I can only say, with the Captain, "it beats me entirely!" WINIFRED, on the plea that "one must have a starting-point," assumes (what I fear is a mere guess) that No. 1 weighed 5-1/2 lbs. The rest all do it, wholly or partly, by guess-work. The problem is of course (as any Algebraist sees at once) a case of "simultaneous simple equations." It is, however, easily soluble by Arithmetic only; and, when this is the case, I hold that it is bad workmanship to use the more complex method. I have not, this time, given more credit to arithmetical solutions; but in future problems I shall (other things being equal) give the highest marks to those who use the simplest machinery. I have put into Class I. those whose answers seemed specially short and neat, and into Class III. those that seemed specially long or clumsy. Of this last set, A. C. M., FURZE-BUSH, JAMES, PARTRIDGE, R. W., and WAITING FOR THE TRAIN, have sent long wandering solutions, the substitutions having no definite method, but seeming to have been made to see what would come of it. CHILPOME and DUBLIN BOY omit some of the working. ARVON MARLBOROUGH BOY only finds the weight of _one_ sack. CLASS LIST I. B. E. D. C. H. CONSTANCE JOHNSON. GREYSTEAD. GUY. HOOPOE. J. F. A. M. A. H. NUMBER FIVE. PEDRO. R. E. X. SEVEN OLD MEN. VIS INERTIÆ. WILLY B. YAHOO. II. AMERICAN SUBSCRIBER. AN APPRECIATIVE SCHOOLMA'AM. AYR. BRADSHAW OF THE FUTURE. CHEAM. C. M. G. DINAH MITE. DUCKWING. E. C. M. E. N. Lowry. ERA. EUROCLYDON. F. H. W. FIFEE. G. E. B. HARLEQUIN. HAWTHORN. HOUGH GREEN. J. A. B. JACK TAR. J. B. B. KGOVJNI. LAND LUBBER. L. D. MAGPIE. MARY. MHRUXI. MINNIE. MONEY-SPINNER. NAIRAM. OLD CAT. POLICHINELLE. SIMPLE SUSAN. S. S. G. THISBE. VERENA. WAMBA. WOLFE. WYKEHAMICUS. Y. M. A. H. III. A. C. M. ARVON MARLBOROUGH BOY. CHILPOME. DUBLIN BOY. FURZE-BUSH. JAMES. PARTRIDGE. R. W. WAITING FOR THE TRAIN. ANSWERS TO KNOT V.