NUTS TO CRACK.

Otago Witness, Issue 3860, 6 March 1928, Page 72

NUTS TO CRACK.

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T. L. Briton.

(For the Otago Witness.) Readers with a little Ingenuity will find in its column an abundant store of entertainment and amuaexaont, and the solving of the problems should provide excellent mental exhilaration. While some of the “nuts’’ may appear harder thaa 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 la their solutions, unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. THE GENERAL ELECTION. As ther e will be a general election this year, it may be opportune to discuss, in the form of a problem, the probabilities of the result, and permissible, perhaps, in view of the fact that parties and not politicians will be referred to. The House of Representatives comprises 80 members, who, it will be assumed, will be formed into four distinct parties, and the prob; lem for the reader to solve is in how many different ways is it possible for 80 members to be divided into four separate groups? For example, it is possible for the whole House to belong to one party, Uz., 80-0-0-0, which would be one wav, just as 20-20-20-20 would be another. The reader should not find this a difficult calculation. For instance, if the House consisted of 10 members only, there would be 286 different ways in which thev could be formed into four distinct parties.

A WHEEL CURIOSITY. Every reader knows that a wheel in one revolution covers a distance equal to the length of its circumference, but has it occurred to him that the hub of the wheel which only revolves once to every revolution of the wheel covers the same distance, yet its circumference is much less m length than that of the rim of the wheel? For example, a wheel 12ft in circumference travels a distance of four yard s ln i °" e ‘’ evo!ut ' on , while the hub of the wheel 2ft in circumference covers a similar distance in one circular motion on j 'Y ls k-! » n tlle reader explain this paradox . Ihtf question raised in this column some tune ago as to whether the top part of the rim of a wheel of a vehicle in motion moves any faster through space than the same part when nearest the ground, will perhaps be found interesting when considering the present curiosity. TYING UP PARCELS. In a certain large printing house, where great quantities of string are used in the packing of parcels for despatch, the management found that much waste was involved owing to parcels containing the same articles and quantities not being packed in the most economical and uniform way. Special instructions ere therefore issued, and this useful commodity “ rationed ” as in wartime days. The incident coming under notice has suggested a useful little problem on the subject. \\ hat is the largest-size package of rectangular form that can be tied with exactly four yards of cord (exclusive of knots and loose ends), if the string passes once lengthways round the parcel and twice round the girth? It will be necessary to find the length, breadth, and thickness of the package, as the cubic capacity only will not be a complete solution of the problem. IN A MILITARY HOSPITAL. Whilst on the subject of war-time happenings, some records of one of the military hospitals may be interesting, and incidentally will form the basis of a little nut to crack. zMthough the calculation in itself is not difficult, the method of easily arriving at the correct solution may prove a little perplexing. Twothirds of the inmates had lost an eye, three-fourths of them were minus an arm, and -.bur-fifths had lost a leg. Assuming that at least twenty-six of these inmates had each lost all three—viz., an eye, an arm, and a leg, how many patients were in the hospital, the number being confined to those mentioned?

A SET OF CHIMES. As promised, here is a poser “ in combinations ” that is not difficult, and should prove very.. interesting:—lt was decided to erect a set of bells in a certain public building suitable for the purpose, and although the peal was to consist of three bells only, and not four, it was nevertheless called by everyone a “carillon.” There was some discussion as to how the peal should be arranged, but ultimately it was decided to construct it according to the following conditions :—First, that every possible permutation of the three bells (that is to say, the different ways in which the peal could be arranged), should be rung once only; second, that no bell should move more than one place at a time; third, that no bell should make more than two successive strokes in either the first or last place.; and fourth, that the last change should be able to pass into the first. The reader will find it quite worth while spending a jittle time on this problem.

SOLUTIONS OF LAST WEEK’S PROBLEMS. THE VAGARIES OF PUBLIC . CLOCKS. The slower clock should be put forward practically eleven minutes five seconds (11 1-13 minutes), so that both would show and strike nine together on Monday night. THAT EXTRA INCH. The extra inch was due to the perimeter of the rectangle being increased by four inches, being 36 inches against that of the square of 32 inches. Of rectangular figures of equal perimeter a square contains the largest area, and in the case mentioned by the correspondent it will be noted that a rectangle 15 by 1 would have the same perimeter as the square, 8 by 8, yet it would only contain an area of 15 against the square’s 64. ANOTHER FALLACY. .If each original square be taken as one square inch and the full area 64 square inches, it will be found that although there are only 63 “ squares ” in the altered diagram, the superficial area remains the same. The curiosity is explained by the fact that the height of the little corner clipped off and placed in another position is greater than the other squares—viz., 1 l-7in instead of Lin. The new form is therefore 9 1-7 multiplied by 7 —viz., C 4 square inches the same area as before. ONE RESULT OF THE DROUGHT. The difference would be £37 6s 3d per annum. A GEOMETRICAL PUZZLE.' Lay a penny flat on the table with two others on top of it, leaving two equal parts of the first uncovered. Then place the other two on edge resting on the bottom coin and leaning on the other at the top. The five pennies will then be equidistant as each touches the other. ANSWERS TO CORRESPONDENTS. “ J.R.G.”—The suitable ones will involve diagrams, hence the difficulty. “ P.T.II.”—It will be fully explained next week. Thanks. “ F.J.C.”—A stone-age problem, possibly antediluvian, yet it still promotes controversy. The photograph Is of the speaker's son, and is not his own. “ Bridge.”—Method has been sent by post as requested.