We see that each of the members present paid 4d. to make up 5s. There must have been 15 persons present when the bill was paid, and consequently 18 at dinner. Now, it is evident that the classes are as 2, 3, and 4, making 4 Officers, 6 Non-com’s, and 8 Privates. Again, it is evident that 5s. being the sum to be paid by 1 Com. and 2 Non-coms.; each Com.’s share was 2s., and each Non-com’s 1s. 6d., and from the conditions of the question each Private’s share was 1s. 3d.; those who remained had to pay. 3 Officers, 2s. each and 4d. each 7s. 0d. 4 Non-coms, 1s. 6d. each " 7s. 4d. 8 Privates, 1s. 3d. " " 12s. 8d. ----------- Amount £1 7s. 0d. (136) The Alphabet. (137) 4 glasses. (138) 37·6992 feet. (139) 157-1/7 square miles. (140) 324. (141) Bottle 2¼d., cork ¼d. (142) 1, 4, 16, and 64. (143) 16 days. (144) 7¼d., 4¾d. (145) 1st, 64; 2nd, 48; 3rd, 36; 4th, 27 gals. (146) 1st £24, 2nd £20, 3rd £8, 4th £28. (147) This is one of those _impossible_ questions that one often hears. The fractions, when added together, equal 19/20. So the whole £1 _cannot be so divided_. The following solution is often put forward:-- ⅓ plus ¼ plus ⅕ plus ⅙ = 20 plus 15 plus 12 plus 10 = 57 -------------------------- -- 60 60 s. 20 x 20 = 400 div. 57 = 7-1/57 to 1st son 15 x 20 = 300 div. 57 = 5-15/57 " 2nd " 12 x 20 = 240 div. 57 = 4-12/57 " 3rd " 10 x 20 = 200 div. 57 = 3-29/57 " 4th " -------- 20s. (148) The locomotive pushes No. 1 truck up to the points, then returns to the opposite siding and pushes No. 2 up to No. 1 at the points; the two trucks are then pulled by the locomotive down the siding and pushed on to the main line to a position anywhere between the two sidings; No. 1 is then uncoupled and left standing, whilst the locomotive pulls No. 2 along the main line in order to push it up to the points where it is left; the locomotive returns to No. 1, and pulling it a short distance, in order to get on the proper siding, pushes it into its required position, uncouples, and proceeds up the other siding to the points to pull No. 2 into its proper place, then uncouples and returns to the main line. (149) 14,400 quarts (150) A, 2s. 7½d.; B, 1s. 1½d.; C, 9d. (151) 1st Company, £2400 2nd " 1800 3rd " 1600 4th " 1500 ----- £7300 (152) Lines, 29; letters, 32.