Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21467, 15 April 1933, Page 5 (Supplement)

Intellect Sharpeners

AGE OF A FAMILY BY T. L. BRITON "F" was born some years beforS his wife, and there are two children in the family, a boy and a girl, the former being the older of the two.When the sister was born, her brother was exactly one-quarter the age of the mother, and at the present time he is exactly one-quarter the ago _ of the father, " age " being in all. instances in this puzzle an even number of years, thus making it easily solved without the aid of either pen or pencil. _ At • present the mother is as many times older than the son as the is older than the daughter, and, curious as .it may seem, the combined ages of the two children are in the same proportion to the age of the father as in the two instances just mentioned.; Taking the combined ages of the family at present, the average number of years is 25, and ten years ago the average of the family was only, three years less than it is now. Tho details given in the last sentence are not essential data, and are added with the object of making tho question more intellect-sharpening, for it is taken for granted that the method of solving the puzzle as suggested by the title willbo observed when the reader is seeking to discover the respective ages of the four people at present. POULTRY AND GROCERY Here are two simple yet useful questions which the reader will no doubt readily answer without leaving his chair to seek pen or pencil. A housewife who was attending the market for the purchase of her Easter poultry acceded to tho request of a neighbour to buy for her three ducks and a paif of chickens, her own purchase being A goose. After the birds had been de- I livered and accounts settled between ? the two housewives, the two husbands y arrived, both, after admiring the poultry 7 , inquiring the cost of them respectively, which was told by the marketing "lady in tho follovring manner:' " Four shillings and sixpence is tjbe price of the pair of chickens, and assuming that the cost of the three ducks is the same as four similar chickens to those bought, and that three geeso of precisely the same valye as the one purchased, cost the sarfte money as ten of the same kind of ducks as the throe in question, the price paid for the goose should b« easily found as well as the ducks." What were the prices ? A grocer bought a quantity of stores ? which he agreed to ppy for in two instalments within 30 days, the contract' being fulfilled to the full amount due, namely, £9O. The instalments were not in equal sums, and the question for the reader to answer a3 Boon as he has perused tho , statement, is, if, the difference between the two amounts is exactly double one of them, what is the amount of the other ? STEPPING THE DISTANCE In the north-western part of a. large square paddock of 25 acres is a sports ground, enclosed by itself in the form of a circle, whose diameter is 160 yds., there being two gates in this fence, one of which is situated due north from tho centre of the ground. With the object of approximately ascertaining the distances between certain points, two groundsmen made a start from the centre of the circular area, one of them proceeding direct north to the gate and thence in the same direction te a point 10yds. outside. From -that point he proceeded in a south-easterly direction to a spot due east of the centre of the sports ground and 40vds. .from the fenced circumference, from which point he proceeded direct south for 160 yds., where he met the other man, who had walked direct from the starting point in the , centre of the area, passing through | the gate situated in that direct like. Both men left the centre at identically the same time, both walking at the same rate throughout, and the simple question to answer is, assuming that Both men proceeded on their respective ways without any perceptible stop, how long did the second walker arrive before the other at the meeting point stated, if the man who had gone through the northern gate took four minutes for the full distance P . The drawing of a simple diagram following this description should enable the reader to solve the problem in quick time. TWO MONEY QUESTIONS Two people had a certain sum of money between them, a similar amount each, and they agreed between themselves that in each of the two transactions under fixed conditions one would forfeit to the other a certain portion of his holding, the particular class of transaction in which tho two persons engaged themselves not being material to this arithmetical puzzle. However, " B " had to forfeit £1 to "A" as the result of the first venture, but .in the second essay the conditions made it imperative that the latter player or speculator should hand over to the other exactly two-thirds of the sum that he then had, which of course included the £1 that. " B " had handed over in the first of the two transactions. The question to be answered, of course from the armchair, is if " B " then held four times the sum that his companion had as a result of the two ventures, how much did they have at first?, Six men were responsible for the payment of a bank guarantee of the " joint and several " kind, each being liable for an equal share of the total sum. When the account was called up one of the party had become bankrupt, with no assets available for the payment of his share of the bond. If this unfortunate position residted in the other five guarantors having to pay £4 each more than he would have been called upon had the six persons shared the amount equally, what was the sun' guaranteed ? LAST WEEK'S SOLUTIONS Constructing a Word. —Tho full won! is " masterly," and the clues " essay," " seainy " and " later." Elementary Arithmetic. —Twelve and six for the " match " balls, and 7s 6d for the others. (2) Five hours per day.. An Alphabetical Sum. —The equivalents of the letters R.S.T.TJ.V.W.X.Y. and Z are 3.7.8.2.9.6.5.4. and 1. respectively. Aunt Tabitha's Age.—Born in January, 1902, the aunt is at present 31 years of age, and the nephew 18 years younger, namely 13, the same digits as the older person, but reversed. A Useful Code—The text is: "In composing code messages in cipher it is immaterial ■ whether we employ special characters to denote various letters or whether we use the letters in a non-natural sense." A capital letter in each of the five vowels was used to denote a different equivalent'to the vowel of smaller type. The ' W ! and ' Y ' have no significance in the code." answers to correspondents " Monetary."—The standard coin of the United States is 10 dollar (eagle), the legal weight of which is 258 grains aud par-equivalent 41s l£d, the sovereign (£1) having, a legal weight or 123.27 grains. C.K.S.—It was stated that there wore two examples, though the foml 1 * tion you mention would hmit it to one. It is not, of course, a mathematical puzzle..