INTELLECT SHARPENERS

Otago Daily Times, Issue 23528, 17 June 1938, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C. J. Wherefore Correspondence should be addressed to Box 1177. Wellington, FOUR GAMBLING MEN Four men. whose initials are A, B, C, and D, had been playing cards, As they had no counters, they took a box of matches, containing 48, and distributed them in equal snares. When they had finished their game, A had 7 more than C, and D had 9 more than B. They did not play any more that evening, but continued to sit at the card table. Only one of the four is a smoker He used two of his matches, and that left him a number equal to that of two of the other players added together, Later on he used another two matches, and that made his number equal to that of the fourth man Which of the four men is the one who smokes, and how many matches had each man when they ceased playing 7 SUBSTITUTION PROBLEM My friend the professor started on a piece of work a few mornings ago before breakfast, the time by the clock in his study being BC minutes after the hour A After working for DE minutes, an interval only F minutes less than a whole hour, he laid down his pen. and remembered that he had not yet had his breakfast Then he noticed that the clock showed HI minutes after the hour G. These nine letters. Ato I, are written in place of the numerals I to IX. each of which is seen to occur once in the narrative. The problem is to assign the correct numeral to each of the letters. ARMCHAIR PROBLEMS A and B were driving sheep in a mob, which included sheep belonging to both of them. They had to camp the sheep for the night in a paddock, of which the fences were not reliable, with the result that several sheep got out and were never seen again. These lost sheep amounted to 7 per cent, of the whole mob, but A’s loss was eight sheep more than that of B. How many sheep were there, and how many did each man lose? Mr Hawker would probably describe himself as an expert salesman. He can persuade his vicitims to man. He can persuade his victims to in the least, and his practice is to obtain from some of his shopkeeping friends a line of goods which have proved unsaleable over the counter, and to dispose of them over the doorstep. Last week he was given a handful of pocket knives to sell. On the first day he sold several, on the second he sold more, so that his receipts included 7d for every fid received on the previous day He sold what was left on the way back to the shop, where he handed over 12s lOd, and asked for his commission. How many did he sell each day, and what was the price he asked? CONTRIBUTED The following problem is contributed by a reader living in a suburb of Dunedin. An officer commanding a body of men in a rather quiet and uninteresting district, tried to entertain himself and his troops by devising new ways of arranging them on parade. On the first day he placed them in 24 squares—that is, the number of men in each row of the formation was the same as the number of rows. These squares were all of the same size. On the second day he did exactly the same thing again, but the squares were now larger, so that there were only six of them. On the third day eight men were absent, either sick or malingering, and this enabled the officer to arrange the remainder in four squares. On the fourth day 14 more men were not on parade, and he found that he could make just two squares with what he had. How many men had he under his command? AN OLD PROBLEM. A correspondent asks for the correct mathematical way of solving the following old problem, of which he has found the answer by simple trial. A shopkeeper reduced the price of his oranges by one penny per dozen, and at the new price the buyers obtained one more orange for a penny than they had received formerly. At what prices did he sell them? The purely mathematical way of solving this will be given next week, after readers have had the opportunity to form their own opinions about it. SOLUTIONS OF LAST WEEK’S PROBLEMS Curiosity.—They are twins, tl years old. Armchair Problem. —The ooy's bicycle cost one shilling more than the other. The prices were £) Ifis and £1 15s. Birthday.—June 2b is a Saturday this year, and 7 times 25 is 175 That day is the 176th ot the year. Motorists.—Yes, the distance may be 70 miles, travelled at 28 m.p.h. in the morning and 35 m.p.h in the afternoon By following up the principle thus indicated ever larger values are easily found Families.—The A family are aged 16 and 3 the B family 8 and 6, the C family 12 and 4 The additional pair must be one adult of 24 with a two-year-old infant, which is venimprobable but not impossible Theatre.—lf the sum o' the numbers is 2 less than the number if pence, the fourth coin must be a sixpence, so that each person paid 6s for seats 70 71. 72 73 If it is 2 less, the fourth coin is a threepenny piece, and each person oaid 5s 9d for seats 68, 69. 70, 71