INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20722, 15 November 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

A REMOTE CHANCE.

Ill' T. L. BRITON

A correspondent, A.V.H.., has Sent a problem asking for a solution of it. evidently overlooking the invariable rule ol publishing solutions only ol' problems appearing in this column, limited time and space necessitating this practice. As, however, the question submitted should be of interest to the render, it has been made the subject of this problem, the solution of which will therefore appear in the ordinary course next week. A.V.H. mentions that an advertising firm has published a sot of faces of eight different types of girls, merely, he says, the outlines, without any features, these being grouped separately, tho firm offering a prize to anyone who succeeds in placing the features in each of the eictht faces correctly. The correspondent s friend says that if a person sent 64 different " plaeings," one of them rntist be right, but A.V.H. thinks thafc 40.320 efforts may be necessary so that the winning one is included. Lot it bo assumed for the purposes of u problem that the eight faces aire real girls who have each placed their pince-ncx on tho table, and try to discover by calculation of course, in how many ways it is possible for every girl to take at random a pair of glasses that does not belong to her. ANOTHER PHOTOGRAPH. Some time ago a question was asked in this column concerning the relationship of two people in a photograph, to whom a third was addressing herself, and upon publication of tho correct answer, a lady, wrote to say " that the solution made one of the parties her own mother"; a comment that is evidence that the question was not as easy to correctly answer as it may have appeared. Here is another which should give the reader some moments of quiet thinking. Margaret held in her hand a photograph of a relative, a young girl who had no brothers or sisters. When showing the picture to Mrs. Smith-Day,, Margaret said to her that the young girl was also related to Madame Smith-Day, for the latter's husband's mother-in-law is the grandmother of her (Margaret's) only nephew, who is a first cousin of the girl in the picture. Margaret is the youngest in the family, which comprises one boy of school age, and three girls, and as she, Madame Smith-Day, and the young girl in the photograph arc relations-in-blood. How are they related respectively ? And who is the girl in tho photograph? ON THE DIAL. Here is a problem that calls for some ingenuity, but involving no mathematical calculation, notwithstanding that it will require some thinking on the part of tho would-be solver. Draw ii circle and place in it the figures as in tho dial of a timepiece, but'omitting the two, four, eight and ten, then draw four lines from tho centre, one to each of the figures three, six, nine and twelve. Take eight counters marked respectively 0, N, S, U, I, C R, and place tho first-named seven on the respective figures one, three, five, six, seven, eleven and twelve in that, order, the R to be placed in the centre. The problem is to move the counters one at a time direct from any figure to an unoccupied one, or to and from the centre along the lines drawn, so that the counters will read, in an opposite direction to tlve movement of clock-hands, C, 0, U, N. T, E. R, S. The conditions that should make this 'puzzlo less easy to solve are that one of tho eight counters is a fixture, and cannot, therefore, be moved, and that no jumping over is permissible. _ if the reader can accomplish the feat in fewer than 17 moves, perhaps he will permit his method to be published for the information of the rest of us. The centre must be unoccupied when completed. FOUR IN LINE. Add two more counters to those used in the preceding puzzle, and with the name sheet of paper, which is no doubt in <i more or less rectangular shape, tho equipment is at hand for this problem. Place five of the counters on the paper along the top edge, with approximately tho same space between them, and the other fi%*e along tho bottom edge in the same manner. The question then is, can tho reader remove four of these without disturbing the rest, and transfer them to such positions that thei whole ten counters will form five straight lines with four in each line ? It merely requires a little patience, together with some ingenuity. After accomplishing the feat try to calculate in how many different ways it can be done, tho two rows to bo in the positions given when starting to make an arrangement that will comply with the conditions set out. HOW MUCH FASTER? The recent public test between two rival motor-cars of foreign manufacture, and the method adopted of ascertained the relative and actual speeds of these machines, suggests an arithmetical calculation which lias the merit of not requiring much figuring, should the reader decide to find the solution by the aid of pen or pencil. The effort, however, should prove more mentally invigorating if the would-be solver will'treat tho problem as suitable for the armchair. The test was over a distance that could be covered in daylight between two points, A and B, the blue car leaving the former place at the same time as the red one left B. If the former arrived at its destination exactly one hour after passing the other, and the latter machine reached its terminal point exactly four hours after it passed the blue car. how much faster did the one machine travel than its opponent ? It may bo taken for granted that it was a non-stop test. LAST WEEK'S SOLUTIONS. Dead Heat in Horse Race.—lm. 30s. for tho mile. Four-hand Oribbago.—When B and I are partners against L, the latter s partner would bo G, provided that when Gr and. B wero partners their opponents were not any of those players mentioned. Obviously with this arrangement tho same four players can never sit together at tho same table moro than once under tho conditions expressed. A Pastime Problem.-~Seventcen _ exchanges are tho fewest number possible; M and S were already in their correct positions. Forming Squares.—Tho smallest number is 160,225 men. A Poser in Combinations. —127. The rule is to multiply together as " twos " us there are curios, and deduct one.