WEEK-DAY CHARITY.

Evening Post, Volume CIV, Issue 20, 23 July 1927, Page 20

WEEK-DAY CHARITY.

As next year commences on Sunday, tlie year 1023 will be selected for this problem. A gentleman had unexpectedly come in for an immense fortune from oilboring ventures, and decided to distribute systematic charity during the whole of the year as a public recognition of his good luck, setting aside a certain sum for this purpose. His method was to dispense the charity on week-days only, Simdays being absolutely "tabu." Supposing the sum were an even numbor of pounds, which, by distributing an equal amount on every day of the year, would become exhausted after the last dole on 31st December, but by eliminating Sundays ana giving equal sums on week-days inly there would be exactly one pound over after the last distribution at the end of the year, what is. the smallest amount that could be donated under these condiin°oo -ii i must uofc bo overlooked that rj-3 will be Leap Year, which makes a great difference, even though the 29th o£ February does not fall on Sunday. THE CHEESE MERCHANT. A cheese merchant always arranged his goods on the shelves methodically'according to weight, the smallest on top. On one shelt he had ten cheeses, arranged as follows: 12 3 4 r, U 7 8 9 10 The numbers representing the number of pounds in each. It will bo observed that besides placing the lightest on top, there w a common difference in the weights of the cheeses iv each tier, and also that eaoh one is greater than its left-hind neighbour. Can the reader determine in how many different ways the cheeses can be arranged, having the smallest on top and each one of higher weight (in both rows) than the preceding one, conn tine from left to right? IN A BOARDING-SCHOOL. A square building connected with a boarding-school had the whole of the iirst lloor divided into nine compartments eight ot which were used as dormitories, the ninth being takeu up by a lift in the centre ot the building. During the ivcent cold southerhes, a number of boys changed into unoccupied beds on the north side and on the first night there were six times as many boys on that side as on each ot the other sides of the house. On tlio next night there were five times as ninny, the next four times, the next night three times the number, and on the fifth night there were only twice as many. The ollowing day the house-master must have heard ot this, for that night each dormitory was occupied by an equal .'umber ol hoys. As none of the sleeping compartments were unoccupied on any of the six nights, what is tho smallest number who could have slept there? A diagram will show that there are three dormitories on each of the four sides, though only eight A WEDDING GIFT. At an annual staff dinner given by a city firm to their employees recently there were representatives of four department* present, seventy-five altogether. Twenty were employed in tho office, eighteen were commercial travellers, twelve indoor salesmen and twenty-five packers and store-' hands. During tho evening a collection was made for the purchase of a weililinc present to one of the RtafF, who was not present, however, £2G 12s being subscribed by tho whole company. Supposing <liat six travellers gave as much as eight nnlesmen, twelve clerks ns much an nine of the former, and five packers as much as four olhco men, how much did each department .subscribe? FOOTBALL SCORES. Some interesting figures of one o£ the first competitions of Association football in the Dominion wore discovered tho other day, and aro published (in part) as a little problem. They are as follow:— P. W. h. D. Tor. A'est. IMs. Auckland .. 3 :t fl 0 7 1 v Wellington .. 3 J. 1 1 2 r> 3 ■ Cunluruury .. ,t 1 ] i a ;t ;i Otagu 3 0 J) 0 1 6 0 Supposing that Auckland defeated Wellington 3-0, it is quite possible to deduct from that score, together with the table above, tho result of each of the other live games plnynd. Can tho reader find what tho actual scores were? LAST WEEK'S PROBLEMS. A Noar Thing.—There must have been 144 who voted at iirst, the 41) new arrivals making tho last division 07 .against 9Gtotal IPS. Tho Circumfercnco of a Sphere.—The six feet added to the steel bund around the earth would make a distance of practically one foot between the earth's surface and tho rigid band. It may seem surprising that only six feet in 25,000 miles could make such a difference, but the rulo applies to any sphere independent of tho length of the circumference. It ia quite easy 1 to work this out with two concentric circles. Peculiar Figures.—Tho other examples are: 17 x 17 x 17 equals 4913; 18 x 18 x IS equals fiß32; 2(1 x 20 x 20 equals 17,570; and 27 x 27 x 27 equals 10,083. Over tho Hill.—-Tho samo number of posts at equal distance apart would be required whether they were erected ilour tlu! cutting or a greater distance over the hill between tho samo points. It may seem paradoxical,'though a diagram showing the cutting as the base of tho hill will make it. clear, for tho posts if erected over the hill would bo at right angles to the base. Military Decorations.—Seven men could hold tho medals \inder tho stated conditions, six with tho V.C. and M.C. and ono with tho V.C. only. ANSWERS TO CORRESPONDENTS. L.W.R.—Tho method of solving the problem of the lizard and tho fly is to find tho length of the hypoteniiHo of a. triangle with its bane equal to half the circumference and tho perpendicular tho height of the cylinder. C.X. —Leap Year is missed once in every hundred years to mako tho calender agree uioro cloßoly with the courso of tho sun. H.P.—Solutions are not required to be ucnt in unless specially usked for.