INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20384, 12 October 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

CANDIDATES' PLEDGES.

BX T. I/. BBITON.

Tho discussion concerning pledges given by Parliamentary candidates, has prompted a problem in mathematics. Let it bo supposed that in a certain province there aro ten electorates each returning one member, tho total number <?f candidates being 27, and that it is immaterial how many contested tho individual seats. Tho various organisations requesting pledges from the candidates represented the following four issues:—(l). Bible in Schools. (2). Prohibition. (3). Conscientious objectors. (4). Publishing totalisator dividends. Assuming that the ten members were to be elected on these issues only, tho problem is in how many different ways can they bo chosen, that is to say in how many different groups is it possiblo for tho ten members to ba. arranged ? For example there could ba five Bible in Schools supporters, five Prohibitionists nnd none for tho other two, or there might be ten in favour of publishing dividends, and none in any of the other groups. Of course it is understood that for problem purposes no candidate supports more than ono of the four issues, thus securing four distinct parties in that province. Though not a difficult " combination" problem, it is quite possible that the reader will require a little time to think it out.

WINNINGS AT TRENTHAM.

One of the courtesies extended to the officers end mon of the German gun-boat Ernden, was an invitation to the races at Trentham. Tho visitors admitted that everyone of them patronized the totalisator. So let us formulate a problem on their results, which we may assume were favourable to themselves, as is usually the case with visitors who invest their money and trust to luck, without being hampered by " information" of alleged " certaintits." Tho number who accepted was 150, made up of 50 officers, 40 petty officers, 36 A.B.'s, and 24 marines, and the problem is to find, with tho following details to help the solver, bow much each of tho four groups won ? Five officers won as much as four petty officers, twelve of tho latter as much as nino A.B.'s, and six A.B.'s, as much as eight marines, the total sum wou by the visitors being £66 10s.

THREE NEW ZEALAND COINS.

There arc three New Zealand coins on (he table and the reader to name them with the following Yew particulars to aid him, the being quite sufficient for the purposo. The sum- of the three of them is equal to the value of the sum of " two current coins " plus the product of the two largest of tho three coins in question, assuming that money can be multiplied by money. The reader may choose for himself whether or 110 tho " two current coins" mentioned are of tho same denominations as any of the three, the subject of this problem.. Second, the sum of those three coins is equal to tho sum of tho two smallest multiplied by tho third, assuming in this case also thai) tho valuo of tho third eojn can be regarded as an abstract number, in order to bring this problem within the tyws of mathematics. The reader should derive some intellectual amusement when trying to find what these three coins are.

TEAM WORK IN OOMPETITIOHS| Tho suggestion that more team work in the musical and elocutionary competitions might prove an interesting cljanga from tho mass of individual contests, anaV that a different method bo adopted of \ awarding marks, offers an opportunity for | a. problem. Let it be supposed that team / A. of picked students are pitted against/ another team, B, of different numerical strengtli, the judging being based afi averages, the total points gained by p team being divided by the number'|f students in it. Each competitor in team A gained five points more than the number of competitors in that team, and each of thoso irt team B won four points more than the number of studonts comprising their team. Now hero is the point. 1? ono of those in B team wero transferred to A team after tho marks were given, and tho samo facts applied as to the relative number of points to the number of competitors in eacn team, the total marks gained by tho two teams combined would have been one fewer than they were. From these facts can the reader say how many competitors were in each team, and what was tho total number of points awarded*?

TWO FOR THE FIRESIDE.

If the reader can answer the following' two questions right oil without the help of pen or pencil, his name should automatically appear in a list of names, the numerical strength of which will perhaps be much less than one containing the names of those who require a considerable time to reach the correct solutions. (1). How much heavier is a brick weighing three pounds, together with one quarter of its own weight, than another brick that weighs only one pound plus threequarters of its own weight? (2). Six years ago a man was five times older than his son, but now he is only three times as old. What are their respective ages now ? Both theso questions require to be thorouglily understood, before _ attempting to find the answers, otherwise wrong solutions may result.

LAST WEEK'S SOLUTIONS. A Party of Six. The tourists left after the third meal on sth instant. On Half " Commons,'l 850 men. Dividing Six Quarta. Eleven operations aro th# fewe»t possible. Three Men's Gold. Under tho peculiar conditions of problem tho smallest number is 15. What is the Maximum ? The highest value is 16s Bd. A demonstrator is liable to be tempted to place the highest valuo on every square allowed by tho conditions. Should he adopt that method tv/o spaces would have to be left blank. All squares are occupied in the correct solution, jvbich gives the highest valuo possible.

ANSWERS TO 00RRESP0NB3HT8. T.C.—The stated sum, viz., 395, was the factor which limited the problem to one solution. " Chorries."—The ratio wm three to two. " Desert Song."—lt is quite possible on your assumption iind may be worth 'investigating. T.A.L.—lnteresting, but your explanv tion is hardly clear enough without further details. Perhaps these could bo sent if available.