A WEIGHING PROBLEM.

Evening Post, Volume CVII, Issue 150, 29 June 1929, Page 31

A WEIGHING PROBLEM.

Four commodities which, may be .called A, B, C, and D were required to bo weighed separately, but the young inau in chargp having a little leisure, and his naturally-mathematical mind prompting him, he decided to carry out the operation by a more circumlocutory method than by making four individual weighings. This is the way he pro-1 ■ ceeded. Ho first placed A, E, and C ; upon the scales and found their combined weights to be one hundred and ninety pounds. B and D were then weighed together, the dial showing their combined weight at a certaia figure which happened to exactly equal the difference between the weight of A and that of C. Now A and B together were found to be exactly one hundred and ftventy-six potads more than C, the weight of B being only one-fourth that of C. The problem for the reader is to find from these meagre details I what is tho exact.weight Of each com--1 modity, their combined weights being i in excess of the maximum registeringcapacity of the scales, which was two hundred pounds. A SCHOOL COMMITTEE. It is not often that we find the number of candidates for a school committeer exceeding the number of available seats, but a case happened in a provincial town not long ago where this was so, the unusual interest having been stimulated by tho raising of the controversial subject "Bible in Schools," which brought out twentythroe candidates for only nine vacancies. The poll was conducted on the usual principle of one, adult one vote with the right to '"plump" for one candidate if desired, or to vote on one ballot parier for any number not exceeding nine. Now it is obvious that with twenty-three.: seeking election a person could vote for one candidate in twenty-three different ways, or for two in two hundred and fifty-three ways, but can the reader find in how manydifferent ways it is possible to vote at the election in the manner prescribed. It is an interesting.-;.. calculation and quite simple. i_ ■. AT WHAT INTERVALS.

Any conditions may bo assumed in formulating a problem, and provided they are clearly and'sufficiently expressed tho solution is bound by them, no matter how impossible they may bb in actual practice. Tor, example, if a problem concerning a foot race expressly stipulates certain conditions and the correct solution reVeal's tliftt one. of the.. runnors covered the last two kuadred and twenty yards of a milo race in- twenty-two seconds, the fact that no human boing had ever accomplished such a feat doea not enter into the matter. A clock problem is in mmd at present in which the correct answer cannot be verified by ocular demonstration on tho dial.- A, man took his chronometer to a watohmakeff to be rogulated because tiiiv hands 5 came" together every sixty-five minutes exactly. Now it is an obvious fact that provided a timepiece is in going, order whether running fast, slow, or keeping correct time, its hands must always come together at precisely tho samo intervals. Can the reader determine what these intervals are? iA COINCIDENCE.

It was' a coincidence when Alfred) Ben, and; Charlie sat down for a little game of cards that each had in his pocket five silver coins, all of New Zealand currency, tho total sum being twenty-four shillings and sixpemcc. The game was played on the plus and minus system, "A" keeping the scores so that no money was produced until the end of the game. It was agreed before starting.that a loss by any 0116 player of six shillings or moro would automatically close the play, but as the heaviest loser at the finish was Alfred, who lost a shilling loss than that sum, no ' interruption took place. Charlie lost sixpence in the competition, and upon placing their 'iuoney on the table at the finish, it was found that accounts could be settled by, merely exchanging coins; thna each "player had still fivo coins at the coiiclusion. Now assuming that before Commencing, all the sums held by the players were different, how much did each then possess, and what were the fcoins? CUITINO DP LOGS.

Tenders were called'for the cutting up into one foot lengths of one hundred and fifty cords of six feet logs. There were several tenders for the job, the successful one being the sawyer who in the previous winter secured tho same owner's contract to cut up a similar quantity into one foot lengths, those logs, however, being all three feet long only. His tender for tho previous job was at the rate of ten shillings per cord, and when putting in his price for the present contract oi six i eefc logs, he based his estimate upon the price paid for the first job, allowing for the difference in lengths, and this was' accepted by the owner. Hero is a little problem on the position. Assuming that the new logs were of uniform, thickness to the three feet logs in the first contract, can the reader calculate- the total sum tho sawyer would be entitled to upon completion of the nevr job at the price stipulated?