INTELLECT SHARPENERS.

Otago Daily Times, Issue 20958, 22 February 1930, Page 21

INTELLECT SHARPENERS.

By T. L. Briton.

STATE LOANS. A student who signs himself “A Seeker After Light” writes When referring to local borrowing, the Minister Finance said that the Commonwealth Government recently issued a Bi per cent, loan at 98, yielding a return ,2 lve f t , or ’ Ending redemption, of to 14s 4d per cent, per annum, a statement which is puzzling us students. The loan being at £2 below par it seems to us that the return to the investor is only £5 7s IJd per cent, per annum, so where does the balance of 7s 2|d come from? As the redemption of a loan occurs only once, we are unable to perceive why that term should be mixed up with the rate of interest, for according to what we learn at the University, the terms ‘ redemption,’ ‘ conversion,’ ‘ maturity,’ ‘ amortization ’ have no real relation to rate of interest. Can you please enlighten us 7”

This pertinent question is published for the benefit of other readers who may desire to consider it before the explanation appears next Saturday, for what the Minister of Finance is reported to have said is perfectly correct. “I FOUND IT.” , Miss H- G. has sent along the followin« ingenious moving counter problem which should interest the large number of readers who find entertainment in this class of puzzle. The correspondent states that the fewest number o! moves she can accomplish it in i« 23, and thinks that perhaps mme reader mi"ht improve on that number. Rule a squire three by three and place lettered counters in squares a's indicated, notion the capital and the small i, one squarl being left black as shown.

THE COST OF TWO TICKETS. Two girl friends went to the pictures one at the invitation of the other, who had with her the exact price of two tickets for the seats they had decided upon taking. Unfortunately, however she lost some of the money on the way this sum being equal to exactly one quarter of what she had left. As her friend had no money with her to make up the deficiency they were obliged to occupy seats in a lower-priced part of the theatre, the whole of their available being spent in this way. Now here is a little poser for the armchair, li the money had not been lost on the way, and the other girl had Is with tota l ?°? ey the two Wends would have had between them would !? ou S h t 0 Purchase another ticket at the price paid for ° f n * tlckets which admitted 1™“:. ~C an . the reader say what these cost if the price of each was Od less than scupyV eatß that th 67 had feuded to A SPEED PROBLEM. 100 miW fr i° m „^ ana t 0 Para is exactly 100 miles in length, and on. every alternate day May leaves N. by her car to drive to P., usually travelling at 30 mil™ aho, f° U tK aßd her - friend June ieaves P. about the same time on her way to N but always travels at a speed,of about oft™ .T an . IGSS than May - and a& often as not they arrive at & spot “ X ” en route at identically the same time, aow let us suppose that on one -eaSaTt ¥&*?■*** esactly 10 minutes past 8 o clock in the morning to travel as usual top and that at predsely £ same time June left the latter place on hoth Wa 7 t 0 N V, l arranging beforehand that WOU d travel unif ormly through-‘-S? 61 * re3p , ectlve mentioned, fl v „ wltho ? t makln g the usual stop at or elsewhere on the road. From these few details can the reader say how far from N. Junes car won! be at five I™! 03 t 0 noon, and what distance the ? d b ® afar 4 three-quarters of an hour before that time? THE MYSTERY OF FIGURES. ' There is no formula by which the following problem may be solved, as it i 1 ?^ 0 ca t°Sory of “ coincidences - m b the Chinese nad Eastern sages de scribe as the “ mystery of figures,” there being no explanation of the why and wherefore of such cariosities. A cotre.pondM, "HX» that is a good example of this, and asks why it is that to find the smallest num oer which when divided by 2,3, 45, or 6 will leave the same remainder (the number itself being exactly divisible by 7), all that one has to do is to multiply the number of figures mentioned—viz. fr—by the last figure, 7, and after addinv L ° mu * ip ! y ty 7. which gives dOl. Well, the “reason” is precisely the same as in the case of two and two equally four, the value of the figures “wTr^V o '-,! In r tlle exa mple given by -tl.ix. it will e found that exactly the same result is obtainable by multiplying the number of the figures, 6, twice by 5 .and multiplying the result by the first figure, 2, adding 1, giving 301 again. But here is a coincidence in figures concerning the more modern system of money where the sum of the individual figures representing pounds, shillings, and pence is exactly the same as the sum of the in dividual figures when the amount of money is expressed wholly in pence. The amount is less than £SOO and more than £5, and the pounds, shillings, and penc« are all represented, the cipher, however not being used. With the exercise of a little ingenuity, the reader should quickly find the amount, which when expressed in £.s.d. is a repetition of the same f ure.

LAST WEEK’S SOLUTIONS. A TEST MATCH FORECAST. The gentleman’s forecast, (a pessimistic one from a New Zealand viewpoint) was 971 runs, which we all rejoice was a long way from the actual figures. His reason, he said, for suggesting such a huge total was that the New Zealand display in the first test made it “ look like that.” ON A WET SATURDAY. (a) Seven wickets had fallen. (b) Eleven. (c) Forty, making a total of 220 for 11 batsmen. TWO FOR THE PRICE OP ONE. £lB7 10s each, showing a profit of £37 10s, when sold singly for £225, the same as that on three sold to one buyer for £6OO. A SCORE AND ONE PAIR MAIDS. The eldest was 26, the youngest 6, the eighth youngest being 18.

THE RESIDUE OF AN ESTATE. X 39 years. 127 years. Z 42 years. ANSWERS TO CORRESPONDENTS. ®-C- There are twelve fundamental arrangements in the examples sent. -io ® e “^° w -”~Two with 18, four with 19, and two with 22. “ Approximation.”—lf the errors in the sides are equal the error in the full areas should be obvious. “ W.R.”—Appeared on February 8. The solution of “ Two Tough Nuts " is held over till next Saturday