Intellect Sharpeners

New Zealand Herald, Volume LXIX, Issue 21296, 24 September 1932, Page 5 (Supplement)

Intellect Sharpeners

ET T. L. BRITON

ALPHABETICAL SUM

!A problem published some timij ago—sent by a .devotee to this column, '""Mark"! —employed the word '* Impersonal " for the purpose of an alphabetical sum, owing to the ten letters in the word being all different, and therefore capable of giving each letter a different digit or cipher value. On looking for another word having ten different letters in it, it was curious to find how few there are, though many with nine. Giving each of these ten letters a different numerical value which the reader must discover for himself, it is found that the word I MP ERSONAL is alphabetically the product of ELANOIRML and " A," from which it is obvious that the multiplier "A" cannot possibly be represented by unity. If PERSONAL bo divided by SON tho quotient will be M L R P N R, with a remainder of 32. The reader has probably sufficient information from what has been stated to enable him to find tho values of the ten letters, but to simplify it, it may bo added that if tlia six letters PKR S0 N bo added together, and the sum of the three letters S 0 N be taken- from that total, the result is 16. Can the reader construct th» sums arithmetically ? LENGTH OF KAURI LO&

A kauri log was lying outside- a Maori pa awaiting measurement preparatory to; being conveyed to the nearest sawmill. Tha. measuring stick used by tho owner of tho log was four yards in length and perfectly straight, and somo interesting figures, which form tho basis of this problem wera collected by making a number of comparisons of tho log and stick while tha Maoris were awaiting the arrival of tha

" official" measurer. Both tlio log and rod had been sawn off square at hot !i their ends, and. when tho latter was placed on top of the log with one end of it extending some distance beyond tha bottom of the log, the distance from tho top of the stick to ihe' top of tho kauri trunk was exactly 30ft. longer than that part of the rod which protruded beyond tho bottom end of the log. But when tha bottom ends of both log and- rod wera placed level, the distance from the top of the stick to the top of the log was five times greater than . that part of tha rod which had extended below the end when making the first measurement... What was the length of the log ? AMUSING PUZZLE

An amusing puzzle has been sent by an anonymous correspondent, " X,'* which, upon looking into has been found to be one that demands quite a lot of ingenuity to solve under the conditions set out. Draw a diagram of a rectangle with 24 cells, six by four, or the use of a draughts or chess board would do equally as well. Mark or number _24 counters, numbered consecutively from one up, and place ono in each cell in the following order:—

3 1 2 15 8 21 17 6 18 24 12 10 13 9 16 4 20 5 19 7 23 14 22 11

The puzzle is to transfer the numbered' counters to their proper consecutive positions beginning with one in; the top lefthand corner, and ending with 24 in the bottom right. An exchange is made by taking a counter in itach hand and exchanging their places. For example 14 now occupies the proper place for number 22, so by putting one in the other's nlace would constitute a " move." The object is to accomplish this in the fewest number of moves, and if any reader can perform the feat in fewer than 17 his method will bo published. AN OLD PROBLEM

One of the more frequent inquiries from, readers is the old question concerning the difference in the time occupied by a steam launch or other vessel propelled for a distance against the tide and returning with it to the starting point, as compared ■with that taken under similar conditions in every way, excepting that the-water is noil-tidal. The question is much older than steam, so let us bring it up-to-date and demonstrate a problem with an aeroplane the solution to be arrived at without the aid of pen or pencil. It travelled from " X " to " Y," a distance of 100 miles with the wind in one hour and 40 minutes, and returned from "Y " _to "X" with the same force of wind against it in exactly five hours. ( The figures have been so stated that tho question may be answered from the armchair, namely, at what velocity did the wind blow, and what time would it take the aeroplane to travel 200 miles when there was no air disturbance whatever, taking for granted the engines in both cases worked uniformly throughout the tests ? QUESTION OP FARE

Hero is a poser arising out of the aeroplane trip which may be answered from the armchair though the reader is warned not to hastily determine the answer, otherwise he is likely to be caught tripping. Supposing that for the trip of 100 miles from "X " to ""i " and back, the sole occupant, " A," agreed to pay a rental of £3O for the machine, and that, upon arrival at " Y " he secured a ,P as ' senger for the return trip from to ,c X." If it were agreed between the two travellers that the passenger '' B " would pav his proportion on the basis of tha amount that "A." had rented the machine for the 200 miles there and back,_ namely, £3O, how much should "A" receive from "B" as his fare for exactly one half the distance travelled by the pilot A . It mav be added that this question, or ona similar to it, was put- to a group of girl students who were amusing themselves' one afternoon with " catch puzzles, and although three different answer;! wera given °by the five girls, the correct one was not forthcoming. This is not, however, a "catch" question, but one of pura mathematics LAST WEEK'S SOLUTIONS

Four Numbers.—" A," 8 ; "B," 6j " 0," 10; and " D," 12: Total 56. Batsmen's Trophies.—" X," 36; " Y," 27* " Z/' 42 —105 runs out of 220 by the team.

Free to All.—The }>igger car caught the other at the 124-mile post, exactly two hours and forty minutes after starting.

Two Curious Arrangements.--252 4 1 4 505 1 0 1 252 4 1 4

Financial Stocks.—(t) The price being £9O, £13,500 would bring in the income required. (2) Fivo per cent at -105 is better than four and a-half at 95. ANSWERS TO CORRESPONDENTS F.S.—Much obligee. "Old Reader."—A series of four will be published during the nest two mont..., all of different classes. " Alphabetical." —Probably two letUjs were transposed, but that yould hardy account for the different construction men tioned. . " , / Space will not permit Rowing the full process, but the method of ing, the carious problem has ?®^ alre sent in your addressed. enjelpE^i