INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20496, 22 February 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

STATE LOANS.

BI T. L. BRTXOW.

A student who signs himself "A Seeker of Light" writes:—" When referring to local borrowing, the Minister of Finance said that the Commonwealth Government recently issued a 5-| per cent. loan at 98, yielding a return to the investor, including redemption, of £5 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 i 3 only £5 7s ljjd per cent, per annum, so where does the balance of 7s come from 2 As the redemption of a loan occurs once only, we are unable to perceive why that term should bo mixed up with rate of interest, for according to what we learn at the university, the terms 'redemption,' 'conversion,' 'maturity,' 'amortisation' have no real relation to rate of interest. Can you please enlighten us V This question is published for the benefit of other readers who may desire to consider it before th'a explanation appears next Saturday, for what the Minister of Finance is reported to have stated is correct.

" I FOUND IT.". Miss H.G. has sent an ingenious moving counter problem. The correspondent states that the fewest number of moves she can accomplish it in is 23, and thinks that perhaps some reader might improve on that number. . Rule a square three by > three, and place lettered counters in. squares a3 indicated, noting the capital and small i, one square being left black a3 shown. ,

The letters may be moved vertically or horizontally to a vacant square, bat nob diagonally, and no leaping over a counter is allowed. To achieve the desired result the letters must be moved in the manner stated, so that in 25 moves or fewer the square will read, 'T found it.", the last space being left blank.

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 intended taking. Unfortunately, however, she lost some of the money on the way, the sum being equal to exactly one-quarter of what she had left. Her friend had no money with her to - make up the deficiency, so they were" obliged to occupy seats in a lower-priced part of the theatre, the whole of- their available money being spent in this 'way. If the money had not been lost on the way, and the other girl had had one shilling with her, the total money the two friends would have had between them, would have been exactly enough to purchase another ticket at the price paid for each of the two tickets which admitted them. Can the reader say what theso tickets cost if the price of "each was sispence les3 than for the seats that they had intended to occupy ?

A SPEED FEOBLEM. The road from Nam* to 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 50 miles an hour, her friend June leaving P. about the same time on her way to N., but always travelling at a speed of about ten miles an hour less than May, and-as often, as not they arrive at a spot "X"*' en route at identically the same time. Suppose that on one occasion May left 2SL at exactly ten minutes past eight o'clock in the morning to travel as. usual to P» and that at precisely the same time June left the latter place on her way to N-, arranging beforehand that both cars would travel uniformly throughout at their respective speeds mentioned, and without making the usual stop at "X" or elsewhere cn the read. Can the reader say how far from X. June's car would be at five minutes to noon, and what distance the two would be apart three-quar-ters of an hour before that time ?

MYSTESY OF FIG-USES. There is no formula by which the fol- : lowing problem may be solved, as it be- ; longs to the category of "coincidences" I which tiie Chinese and Eastern sages i describe as the "mystery of figures," j there being no explanation cf the why ! and wherefor of such curiosities. A correspondent. '"H.K.." sent an item re- ! cently that is a good example of this, I and asks why it is that, to find the I smallest number which, when divided by 2, 3, 4, 5 or 6, will leave*, the same remainder —the number itself being ex'actiy divisible by 7—all that one has to do ia to multiply the number 'of figures men- ; tioned, viz., 6, by the last figure, 7, and ; after adding 1 to multiply it again by 7, . which gives 501. Weil, the "reason" 13 ' precisely the same as in the case of two j and two equalling four, the value or the figures making it so. In the example j given by "H'.'K." it will be found that ■ exactly the same result- is obtainable by multiplying the number of the figures, 6, twice bv 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 sysj tem of money, where the sum of the in- ' dividual figures representing pounds, shillings and pence is exactly the same as i the sum of the individual figures when j the amount of money is expressed wholly lin pence. The amount is iess than £SQO | and more than £5, and the poundo, shH- , lings and pence are all represented, the i cipher, however, not' being used. 'With i tiie exercise of a little ingenuity, the reader should quickly find • tha- amount, i which when expressed in pounds, shillings and pence is a repetition of the sama figure.

LAST WEEK'S SOLUTIONS.

A Test Match Forecast. The mail's forecast—a pessimistic ona from a New Zealand viewpoint—was S7l runs, which wo all rejoice was a loug way from the actual figures. His reason ha said for suggesting such a huge total was that the iNew Zealand display in tha first test made it "look like that."

Oil a Wet Saturday. (a) Seven wickets had fallen. (b) Eleven, (c) Forty, making a total of 220 for 11 batsmen. The Residue of an Estate. X 36 years. Y27 years. Z42 years. ANSWERS TO CORRESPONDENTS. C.C.—There ara-twelve fundamental ar- „ rangements in the examples sent. " Benbow." —Two with 13, four with 19, and two with 22. " Approximation "—lf the errors in the sides aro equal, the error in the full - areas should, bo obvious. '• W.li." —TliO solution appeared on February 8. "Two Tough Nuts/-'—Solutions j»ill appear on itarcti 1> :