NUTS TO CRACK.

Otago Witness, Issue 3875, 19 June 1928, Page 18

NUTS TO CRACK.

By

T. L Briton.

(Fob the Otago Witness.)

Readers with a little ingenuity will find tn ils column an abundant store of entertalnmer* and amusement, and the solving of the problems should provide excellent mental exhilaration. Wiliile 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 ■uts."

Readers re requested not to send in their solutions, unless these are specially asked for, but to keen them for comparison with those published m the issue following the publication of the problems.

TWO POPLAR TREES. Two poplar trees growing side by side were planted in 1914, just before the Great War, but did not grow uniformly. Four years afterwards they were measured, and again in 1928, and a perusal of these records (the only ones available) prompts a useful problem. The difference in their heights at the first measurement was exactly one-eighth of the sum of what they were when the last test was made, and during the period that elapsed between these measurements the annual increase in the height of the , shorter tree was one foot, whilst the other added to its stature eighteen inches each year. Now,, if both the trees, continue to grow at the respective rates mentioned for the next ten years, the smaller one’s height in 1938 will be exactly five- i eighths that of its companion. From these recor.ds can the reader determine their heights when the two poplars were last measured—viz., at fourteen vears old? FIELD ARTILLERY. A number of batteries of field artidery, six guns comprising a single battery, were, on a march. Although the roads in places were very rough, the drivers managed to maintain a uniform distance apart, and this latter fact suggests a problem., The distance between the guns of each battery was uniformly one-third of that between the rear gun of one battery, and the leading gun of the battery immediately behind', and the time occupied by the whole force in passing a fixed point was 51 minutes. If, however, the distance between all the guns • of the-force had been equal to the distance between the guns of a single battery, the time occupied in passing a given point would have been only 39 minutes. In determining how many guns there were altogether the reader may ignore the actual space occupied by a gun itself. NUMBERED CUBES. If a set of dice be properly made they should be perfect cubes of uniform weight, each correctly numbered one to six on its respective sides, so that any game played fairly with them should not favour one player at the expense of another. Still it is possible for a blindfolded person to tell what is the result of a throw—-that is to say what numbers fall uppenjiost —this being revealed to him by the use of a little arithmetical formula. Supposing, for example, the numbers thrown are three, six, and four which the operator uses in a simple calculation in addition and multiplication, telling the result to the person blindfolded. Can the reader discover how the latter can correctly determine the numbers uppermost on the dice with nothing to guide him except the result of this little sum calculated by another person', which result in the case given is 6147 TWO. BOYS AT VARIANCE. Two boys, each of whom had been given his first timepiece in the form of a wristlet watch, checked together the

time that a city clock took to strike six the other evening, and they both agreed that exactly 30 seconds elapsed from the instant the first stroke-sounded to the sixth. But that night during the hour given to solving “ puzzles and paradoxes,” in which the family joined, the two boys could not agree as to how long the clock would take to strike 12 at the same rate as it had taken to strike six. In fairness to the elder brother, who was wrong in his answer, it should be stated that later in the evening he got “ even ” with the little chap when the father submitted that old query, viz., which is the heavier, a pound of gold or a pound of feathers-?... These two simple questions can quite easily trip anyone who does not give thought to them, but takes them for granted.

A. TIME LIMIT. As in most building contracts, there was a time limit for the erection recently of a bungalow in one of the suburbs. The. contractor employed from the commencement of the job 15 men who each worked one hour overtime daily, viz., nine hours. When two-thirds of the specified time had elapsed, the builder found that only three-fifths of the work had been completed. He then put on three extra men, no more being available at the time, but, upon making a calculation lie found that at the same rate of progress per man, the job could not be finished in time with 18 men. After consultation with the workmen they all agreed to work overtime in addition to the extra hour stated, and the building was completed in the specified time exactly, without any margin. On the assumption that the 18 men worked' uniformly throughout and at the same speed as the fifteen, how many hours overtime were worked after the three extra men were put on?

LAST WEEK’S SOLUTIONS. A CHIMING CLOCK. The interval between the strokes of the clock which kept correct time and struck uniformly was practically five seconds the fraction of about one-three-hundredths over being ignored. THE ALPHABET. Under the conditions stated there could be 676 different pairs which would of course, include the same letter repeated. Otherwise there could only be 650. A DEAD HEAT. 106-2-syds. TESTING LIQUORS. There were eight gallons in the keg and four in the jar. A SEE-SAW. The boy was sst 101 b, and the method or arriving at the result is as follows: — 25 blocks at 41b each, 1001 b; and 10 blocks, 641 b; multiply these and take the square root. ANSWERS TO CORRESPONDENTS. L. L. du C.—The answer and proof have been sent. H. C. C.—Your favours always welcome. M. du C. —It is a perennial, and probably the most discussed question in problemdom, the majority of people seeming to favour an incorrect answer. A simple yet conclusive proof has been sent as requested.