INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20306, 13 July 1929, Page 27 (Supplement)

INTELLECT SHARPENERS.

A PROBLEM IN PRESERVES. BY T. L. BEITON. A " home-mado-goods " street stall con« iained only tlireo varieties of goods, which tho holder had made herself viz: chutney, marmalade and pickles. By noon tho whole stock was sold. Somo people bought a bottle of ono kind, while quite a number purchased one bottle of eaph of two or tlireo varieties. Let it bo assumed that two-thirds of tho number of purchasers each bought a bottle of marmalade, that throe fourths bought a bottlo of chutney, and that four-fifths took a bottlo of pickles. All the buyers thus did not limit their purchases to ono bottlo for at least 26 of them must have bought ono of each variety while many others must have taken ono each of two kinds.' if no ono purchased more than ono bottlo of any one variety, how many buyers wert there ? TWO ROWS OF BOOKS. " 'Jauranga " has sent,a problem, which appeared in " Elementary Knowledge." lie states that quite a number of persons to whom it has been given were unablo to' discover nil the examples, which tho statement of tho question demanded. There are nino books numbered one to nine respectively, on two shelves, four on the top and five oh the lower shelf—tho former being numbers 2, 9, 4, 3, in that order, while the bottom shelf contained book's numbered 1, 7, 6, 5, 8, reading from left to right. These two rows of figures represent a vulgur fraction equivalent to one-sixth, and it is possible to so re-arrangc tho books that the numbers will represent in this way 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, and 1/9. In these eight arrangements there is only ono in which the figures of either tho numerator or denominator aro in order, that is to say that each succeeding figure is greater than tho one immediately preceding it. Can the reader say what ar« rangement it is ? FAST AND SLOW WORKERS.. ; Tho estimated quantity of earth to be excavated in digging a drain was 480 cubic feet, for which tho lowest tender of £2l 6s was accepted. The man securing tho contract was a novice at .this class of work, and as. there was a time limit he was unablo to carry on without assistance But the expert drain digger, whom he employed saw the situation and dictated his own terms to which tho novice agreed, the money being divided at the completion of the work on the following basis: That the novice could dig as fast as tho other could shovel, the latter's rate of digging, however, being; exactly four limes as fast as the novice could shovel the earth away. Assuming that both worked throughout at this rate, and that their relative, abilities for work were the same in digging or shovelling how should the £2l 6s bo divided? POOTBALL SCORES. Last Saturday's Rugby football scorn revealed several curious .features. For the purposes of a problem let us take the points scored bv each of five teams, A. B, C, D and *E. A scored one less than one-third of D's total and three less than half the number ' scored by ,E team. B's record, phis the points obtained by D, outnumbered the combined totals- of C and E by threo points, the score obtained by C added to by D being one'less than half the srlThfl total scored by tho five teams. If E'a score added to C's represented sevensixteenths of the combined total, and if one of the teams secured exactly onefourth ot tho total of the five together, can the reader find the score of each team!! ■ -■•': CURL AND HER MOTHER. A girl when only half the age she is now was exactly one-fifth'as old ns her mother. At present her age in years is one-third that of her parents. Tho question to decide, sans 'pen or pencil, is how many years must pass before the girl's age is two-fifths that of her mother, and how old will she bo then, if their combined ages, three years later vill be sixty-two years? LAST WEEK'S SOLUTIONS. Brothers and Sisters at Tennlfl. '; ;*, Henry and Joan; Max and Marie; Owen and JEthc-l; Mervyn and Betty. Augustus and Caesar. The men adopted tho following method of travel and both reached the railway station at exactly 3.20 p.m. Augustus rode eleven and one-ninth miles, left the bicycle and walked the <rest of the way, while Caesar walked the former distance and rode eight and eight-ninth miles. Cashing a Cheque. The amount of the store account paid was £4 10s. »d— .»■■ Novel Problem Game. If the iirst player leads oft' with 4 and makes 11, 17, 24, 30, ho nust always win. An opponent making 31, there is only ono number to - respond with viz: 3,- which tho other cannot use under the rules, as a counter may not be played twico in succession on tho same number* Step-Ladder Puzzle. Number tho steps 1 to -10, and the! following method will accomplish tho teat under tho conditions—l and Mum to floor, 1, 2, 3 return to 2; 3, 4, 6, r* turn to 4 and so'-on. ANSWERS TO CORRESPONDENTS, «' Mrs. Ford".—One of the " Menfl Wives of Windsor." " Measurer."—A " palm"„measurement! is threo inches, and a ? hand fow inches, but tho former is practically obsolete. «' Mexico.''—The French metrio system; has been legally established m Mexico, but old Spanish weights and measures aro still in use there. J S H —Tho description of the unmea-. surcd*land is quite sufficient, bnt a rough sketch would mako it easier for a bih>. voyor to identify the boundaries desired. Astronomy.—Named after tho astronoJ?vfiS whoso "cycle" system, has been universally adopted. Tho period is nineteen years. tag --Tho correct solution of tho enigma sent is " Bell," but the diagram would bo too complicated to produce, without which tho enigma would not. be oi interest. Thanks. Student.-" A solid anglo" is formed by sovoral planes on other surfaces meeting at one point. ___________—«.