"NUTS!"

Evening Post, Volume CIX, Issue 45, 22 February 1930, Page 29

"NUTS!"

INTELLECT SHARPENERS All . rights reierved.

(By T. 1* Briton.)

Readers with • Uttlt Ingenuity will tad In thi« column an abundant store of entertainment and amusement, and the solving ox the oroblems should provide excellent mental exhllaratloa While some of the "nuts" may appear harder than others, It will be found that none will require a sledge-hammer to crack them.

STATE LOANS,

■V 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 five and a quarter per cent, loan (SJ) at ninetyeight, yielding a return to the investor, including redemption, of five pounds fourteen and fourpencve per cent, per annum, a statement which is puzzling us students. The loan being at two pounds below par, it seems to us that the return to the investor is only five pounds seven shillings and a penny three farthings per cent, per annum, so where does the balance of seven shillings and twopence farthing come from? As the redemption of the loan occurs once only, 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,' 'amortisation' have no real relation to rate of interest. Can you please enlighten us?" 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 stated is perfectly correct.

"I TOUND IT."

Miss H. G. has sent along the following 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 of moves she can accomplish it.in is twenty-three, and thinks that perhaps some reader might improve on th.at number. Eule a square three by three, and place lettered counters in squares as indicated, noting the capital and smail i, one square being left blank as shown. |i| n d " I t of v I The letters may be moved vertically or horizontally to a vacant square, but not diagonally, and no leapingl over a counter is allowed. To achieve the desired result the letters must be moved in the manner stated, so that-in twentythree, moves or fewer the square will read "I found it," the last space being left blank.

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 monoy 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 wero obliged to occupy seats in a lower-priced part of the theatre, the whole of their available money being spent in this way. Now here is a little poser for the armchair. 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 these cost if the. price of each was sixpence less than for, the, seats, that they had intended to' occupy? "

A SPEED PROBLEM.

The road from Nana to Para is exactly one hundred miles in-length, and on every; alternate day May leaves N. by her car to drive to P., usually travelling at thirty miles an hour, her friend June leaving P. about the same time on her way to N., but always travelling at a speed of aboiit 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. Now let us suppose that on one occasion May left N. 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 behorehand that both cars would travel uniformly throughout at their respective speeds mentioned, and without making the usual stop at X or elsewhore on the road. From these few details, can the reader say how far from N. June's car would be at five minutes to noon and what distance the two would be apart three-quarters of an hour before that time?

THE MYSTERY OT FIGURES,

There is no formula by which the following problem may be solved, as it belongs to the category of "coincidences" which the Chinese and Eastern, sages describe as the "mystery of figures," there being no explanation of the why and wherefore of such curiosities. A correspondent, "H.K.," sent an item recently that is a good example of this, and asks why it is that to find the smallest number which, when divided by 2, 3, 4, 5, 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., 6, by the last figure, 7, and after adding 1 to multiply it again by 7, which gives 301. Well, the "reason" is precisely the same_ as in the case of two and two equalling four, the value of the figures making it so. In th« example given by "H.K." it will be found that exactly the same result is obtainable by multiplying the number of the figureß, 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 individual figures when the:amount of money is expressed wholly, in pence. The amount ia less than, £500 and more than £5, and the pounds,;shillings/a«d pence are all represented, the-cipher, however, not being .used.:, 'With the exercise of a little ingenuity, ;the leader should quickly find the amount, which, when expressed in,£ s. d., isra'repetiI tion of the same figure. '

LAST WEEK'S SOLUTIONS,

A Test Match ForeCast.---Tlie 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 saitf, for suggesting euch 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 ..-two, hundred and twenty for eleven batsmen. Two for the Price of One.—£lß7 ,10s each, showing a profit Of £37;10s when sold singly for £225,' the samp as that on' three sold to" one'buyer'for £000. ■• , ' A Score and One Fair Maids.—The eldest was 20, the youngest 0, the;Bth youngest being 18.., iThe; Residue bf ; an.lEstate.—X :36 years,; Y27 years, Z 42' years. ' "■': ' ANSWERS. TO CORRESPONDENTS. C.C.--There;,are' twelve fuiidainental ar- . rangoments iii the examples sent. "Benbow?' —Two witlv.'.'lß,. .four .jwith 19 and two with. 22.. ....- ...,; ' "Approximation"—lf the -errors in the sid.es are equal tho error in the full. areas should bo obvious. "W.R."—Solution appeared on Bth February. "Two Tough Nuts." —Solutions held over till next Saturday.