NUTS TO CRACK.

Otago Witness, Issue 3808, 8 March 1927, Page 28

NUTS TO CRACK.

By

T. L. Briton.

(Fob thi WiTNßsa.) Reader* with a Httle Ingenuity will find in lis column an abundant ■tore of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the “nuts” may appear harder than others, it will be found that none will require a sledge-hammer to crack them. Solutions will appear in our next issue together with some fresh “nuts.” Readers -re requested not to send in their solutions, unless these are ■pecially asked for, but to keep them for comparison with those published in the issue following the publication of the problems.

THE TWO WALKERS. The highway from A to B is perfectly straight road, and one side of it, 12 feet wide, is railed off for the use of pedestrians, the motor traffic on the road being very heavy. Two gentlemen, G and II invariably walk to business. Going in opposite directions they always meet at the same spot, X. This is not mere coincidence, because they arrange to leave home at precisely the same time, and each regulates his pace to three miles an hour exactly. On one occasion G was 10 minutes late leaving home, but H left at the arranged time as usual. If they both walked at the customary pace—viz., at the rate of three miles an hour, how far 'from X did they meet ? BUDDING MATHEMATICIANS. The price of a pear that a boy was eating gave rise to a little arithmetical parley between the possessor and another lad who had asked how much it cost. The purchaser told the inquirer that the pear cost exactly the discount at 2£ per cent, which he had received when paying a bill for his mother, the amount of this account being exactly what three and a-third dozen pears would cost. “Then,” said the other, “the man who sells them would receive for 10 dozen pears, just half as many shillings as the number of pears he would give for the amount of your mother’s account’” After a little thought the other replied, “Exactly,” How much did ■ the boy give for it? A clear head is essential in solving this, especially if pencil and paper be barred. ON THE . DRAUGHT-BOARD. A diagram is not necessary to illustrate the . following problem if we adopt the American system used in chess, of lettering and numbering the squares for identification. As most readers know, the eighth vertical columns are lettered A- to 11, and the horizontal rows numbered 1 to 8; thus the fifth square in the top row is IE and so on. The problem is to place eight men on the board, so that no two of them will he on the same line, horizontally, ■ vertically or diagonally. If the eight men arc first placed in the top row, it is quite an interesting puzzle to sec how many moves' it will require to place them in the desired positions, moving the pieces one square at a time in any way desired. Can any reader do it in 28 moves? EVERYONE SHARED. There was a crowd of people—men, women, and children —standing outside the gates of a large factory on a very wet morning just before last Christinas. A gentleman, passing by, inquired the reason for the 'crowd, and learnt they were all after jobs. He asked one man how- many people there were altogether, and, after counting them, was told exactly 200. He then stepped across to the bank opposite when after changing a ten-pound note into shillings and sixpences, he re-

turned, and in the true Christmas spirit divided the whole sum between them, giving 3s to each man, 2s to every woman, and 6d to each child. Now, there were five women for every one man, and 14 children for every five women. What were the respective numbers of men, women, and children in the crowd? CHRONOMETERS. At noon on the Ist January, 1899, three chronometers, -which may be called X, Y, and Z, were set going. At midday on the second, exactly 24 hours afterwards, it was noted, that X had kept perfect time, Y had gained 30 seconds and Z had lost as much as Y had gained. Now, supposing that Y and Z had not been regulated, and that the three chronometers had been allowed to keep going without stopping, maintaining precisely the same rate as in the first 24 hours, there would be some date ahead when the three of them would all show identical time together as thev did on January 1, 1899. When did this first occur? Although not a difficult problem mathematically, there is just one pitfall into which the solver is liable I? scumble unless he is very careful. SOLUTIONS OF LAST WEEK’S PROBLEMS. THE TOTALISATOR. £lO on Diogenes. £6 on His Eminence, and £4 on The Captain. These investments would secure a return of £3O whi< -> ever horse won.-tind as the outlay wool! be £2O, a net profit of £lO is thercl.v secured. CYCLING. Irrespective of handicaps, there must be the same number of riders ahead of one man as behind him on a circular track. In the race in question there were 11 riders, half of those in front >f Lamb—viz., 5 added to 3-5 of those behind him—viz., 6—making the total stated. DUCK SHOOTERS. The two boys first rowed across, and one brought the canoe back. Orfe man then rowed himself over, the other boybringing back the canoe. The two lads row across again, and the same process was followed to get the other man across, and finally the two boys. The canoe was left where they found it when the party returned to their camp. A REFERENDUM. A • • .. 19,560 votes. B •• .. 31.060 votes. ' C • • 28.140 votes. II .. .. 30,700, votes. Total . . 109,460 votes. TENNIS. Let us call the four ladies L, A. D, and x, and the gentlemen G. E. N, and T. If ' the games be arranged as follows, it will i)c round that no one plays twice either with or against another, and each person plajs on each day of the tournament. No. 1 court. No o eo ,, rf . Ist day—GD v. EY EL*v NY 2nd day—GY v. NA - TL vF» 3rd day—GA v. TD NL v. TA