INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20538, 12 April 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

A WIDOWER'S WILL,

BX I. L. BIUTON.

When Brown, a .widower, ma<?e his will, ho was sixty years of ago, equalling the combined ages of his fouivcnildren. Tlio will decreed that tho whole estate was to be divided equally between the four of thorn in the year that tho youngest child became tho sarno age as the eldest was when tho will was made, tho widower dying exactly two years after that time. Two years before his death tho ago of tho eldest child was twico that of tho youngest, also twothirds of tho combined ages of Jhe other two, and half that of tho otlic:: three together, there being then foui!* years and six years difference between tlio ago of tho eldest and those of tho sjeond and third child respectively. If :ho united ages of the two latter at that timo were just thrco times that of the youngest, now old was tlio last born when tho estate was divided as decreed ?

SEVEN SQUARES. A moving-counter problem which calls for botli ingenuity and patience, is tho " Hindu seven squares with a limit of ten moves to solvo, and as its equipment requires nothing beyond a fen' counters with pencil and paper, it makes an excellent gamo of "solitaire" available anywhere. Mako a diagram of seven squares in a row numbering them ono to jeven. On the second, third and fourth place counters marked o. lc. a. respectively, and on squares five, six and seven tlio respective lettered counters u. E. r. should bo placed leaving tho first square blank. Tho problem is to arrango the counters in ten moves, so that they will read " Eureka," with tho seventh square blank instead of tho first one. The moves may be mado in any direction ono at a time to an unoccupied square, and one or two counters may be jumped over to reach a blank space. Can tho reader, complying with theso few stipulations, accomplish the feat in i:on moves? Tho two " E's," one a capital, should be noted.

SHOPPING SEPARATELY, A mother and daughter wont shopping together, but had left it so late that thero was not sufficient time t:o complete their business before the stores closed. It was therefore decided to shop separately, tl)o whole of the money they had, consisting of ten shilling notes and half, crowns only, which were divided equally. Upon returning homo it was found that they had each spent exactly, the same amount being in each caso half of the sum taken out. Thero is a useful as well as_ an interesting calculation involved in this episode, if we assume for problem purposes that e?ch lady spent as many ten shilling notes as the number of even pounds in the total sum taken with her, and had also spent one-fifth aS' many half-crowns as the number of pounds stated. The silver coins eacli had over were five single shillings, and on this assumption can tho reader find what sum was spent by each lady?

PUKE MATHEMATICS AND ENGLISH.

A correspondent " Cosmos " has forwarded Sam Loyd's " Mary and Ann " puzzle stating that he cannot now find the answer and asks for its publication. This makes an excellent brain-teazer, and when tho composer sent it to a French friend, he designated it " Tres difficile," which most people think it is, yet tho statement of it is in pe:rfect grammar and the calculation involved is pure mathematics. So if tho reader, after providing himself with a supply of wet towels, will note, carefully the tenses of the verbs used in the statement, the difficulty should be overcome, Tho combined ages of Mary and Ann are* forty-four years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was threo times as old as Ann. When the reader essays to tackle the question " How old is Mary?" ho, should, for the t:imo, forget that it has floored many good men before him.

tflß ELDER SPOUSE. While in the vein, hero is a much easier tangle for the reader to unravel. The first of January was the twenty-fifth anniversary of a couple's wedding day, the wife being then exactly twice as old as tho number of years representing tho difference of their ages then, and on that eventful occasion twenty-five years ago their united ages wero two years more than the wife's own ago last New Year's day. Should the reader consider that these details are not sufficient to enable calculation to lie made determining which of the two is the elder, and by how many years, it may bo added, that the eldest son was born on his mother's ninetheenth birthday in 1906. Can tho reader answer these two questions ? c , NO FORMULA -FOR IT. Although there is no formula by which it may easily be found, the relaxation that tho reader will derive from his efforts to discover tho curious number by a series of methodical trials should induce him to tackle this interesting problem in that way. The number is a lonely one because lliero is none other until we reach tho largo number represented by tho year when tho French first occupied Strasliurg, namely, 1680. This number and the smaller one which the-reader is asked to find both havo these peculiarities, namely, that if cither bo increased by tho digit one, a square number is tho result, while adding ouo to half of either produces tho same effect in both case?. What is tho smaller number, which obviously must bo an even - one, and is uyder 200 ?

LAST WEEK'S SOLUTIONS

Olympic Aspirants. Both started and finished with an equal number of points, viz., 100.

Four Trays of Coins. T4O, 1136, A6O, Y72; Total 216

Queer Relationship Queries,

(1). Fred is a son of Mary Jones who had married a man of tho same surnauio as herself, 110 is of courso a nephew of Richard, but tho problem read " both " not " either."

(2). Jackson's first wifo died, after which ho married her sister, and ho died leaving a widow. Hinder theso circumstances it was correctly staled afterward that ho had married his widow's sister, previously of courso. Pennies and Halfpennies. In a box sin. by 3in., 15 halfpennies can bo placed flat on tho bottom without their edges overlapping, but only eight ponnies can lie so placed. Tlio box would therefore hold 150 of tho former or 64 pennies, being ten and eight deep respectively. The boy's father had thcroforo nothing to pay.. ANSWERS TO CORRESPONDENTS. E.M.i Paeroa. —Items will bo looked into. (2) Seo above. Thanks. " Perimeter." —Tho inner circle has half fho diameter of tho whole wheel, and therefore half tho circumference. A.R.—You still would havo seven to fill tho gaps on your own arrangement of the, figures. There is no other answer, " Charades."-—lt is understood Hint No. 2 is capable of solution, according to tho correspondent forwarding it, though ho is unable to fathom it himself. ( Heart* ache" is one of tho several possiblo bolu* tions roceived, but it hardly fits*