NUTS TO CRACK

Otago Witness, Issue 3890, 2 October 1928, Page 15

NUTS TO CRACK

Bv

T. L. Briton.

( For rai Otago Witness.) Readers with a little ingenuity w.ll find in thia column an abundant store ot 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 are requested not to send in their solutions, unless these are specially asked for, but to keep them '■ for ccfmparison with those published in the issue following the publication of the problems. A GENEROUS CLAUSE. A wealthy Australian grazier who left £1,000,000 or more in cash, property, and stock, did not, when making his will, forget the men who had assisted .him in accumulating - this wealth, and a generous clause dealing with the distribution of one part of the estate, viz., tlie whole of the sheep on the “ back ” station, is worth using as the basis of an interesting problem. There were 15,400 sheep on that area, and the clause in the will stated that the whole of the flock should be divided between the men who had served the grazier for 20 years and upwards, and they were to share in proportion to the number of years they had worked on the station. It appears that there were only three who could claim this distinction, the total number of years the three men had been employed being 105 years. For every 80 sheep Ben received Bill got 60, and for every 120 to whiclr" Ben was entitled old Bob got 140. From these meagre details can the reader say how many years Bob, Ben, and Bill respectively had served on the station? THE SAME BOTH WAYS. The individual figures of 10666612 total 287 This number represents the pence in the sum of £44,444 4s 4d, and it will be noted that the individual figures in that sum also total 28. It is a curious coincidence. There are fewer than five other examples of the same thing. One of them is an amount under £lOO, where the three denominations, viz., pounds, shillings, and pence, are represented, the sum being, as in the above case, a repetition of the same number. There is no formula to guide one in discovering this other example, and for that reason the mystery of it will have to be revealed by a system of trials ’’ which will perhaps be no less interesting on that account. But let the reader make the trials methodical, not haphazard guesses, and he will get heaps more enjoyment from it. ° A HARD NUT. “ Counter-njoving problems ” writes a correspondent (when referring to one entitled “A Feat” that appeared in this column recently), “are to me always a source of enjoyment and very welcome in my little circle.” Well, here is an equally good one of the same l aracter which I have called “ A Hard Nut ” for it really is. Make a nine square diagram three by three and letter eight counters with the eight letters of the name title These should have appeared in their proper order, but by some mischance all the letters were transposed, and read u.u.N.t.a.H.r.blank.A. As shown in the diagram instead of the wav the three words should be written with the blank at the end, viz., the bottom square on the right. . Half an hour’s exercise of patience with a sprinkling of ingenuity should enable the reader to accomplish the change in 23 “ moves,” each “ move ” -being merely sliding a letter to the blank space adjoining it, perpendicularly or lioiiziontally. If he should succeed in fewer than 23, perhaps he will pass the secret on for the benefit of the rest of us.

TWO “ FOURS ” AT BRIDGE. A certain suburb not very far out is the region of abode of four gentlemen who are looked upon by those who ought to know as experts in the gam e of bridge, as well they should be, for they have long studied it both in theory and practice. And what is even a more interesting fact is that each of their wives has also a thorough knowledge of the finer points of the game. Yet, strange to say, when it was resolved that the eight should engage in a tournament, these adepts could not arrange the “ draw ” under the exact conditions they themselvesJmposed It would be a simple matter, they all agreed, so to arrange the games that no person should play either with or against another more than once, that the tournament should proceed at both tables for three consecutive evenings and that every player should take part on each of the three occasions, but when Madame X proposed (and it was carried unanimously) that no gentleman should play with or against his wife, there came the “ rub ” so far as concerns the arrangement of the games. And that’s why the reader’s assistance is now sought. Can he help these “ bridge ” enthusiasts?

“ BOXED ” SHEEP. Sheep are liable to get "boxed” /or mixed when travelling along unfenced stock routes, especially if the grass happens to be succulent, when they quickly spread over the run and ultimately get “ boxed” with the “ resident ” flocks. Here is a nice little problem on the subject, where sheep of four different owners got “ boxed,” the number belonging to each flock being the same. As there was no large yard to hold the lot, when the drovers tackled the task of separating the sheep the four mixed-up flocks were placed promiscuously into four small yards, A, B, C, D. There were 240 more m-yard A than in B, but no other details are avail able except that each yard held a dif ferent number, and it- was required to draft them so that each enclosure contained the same number. One quarter of those in A were drafted into C. This made the number in A and D together equal to the number that were then in B and C. One third of what D contained were also drafted into C, from which exactly one quarter of the then total was* put into enclosure A, and thereupon one fifth of those in A was drafted into yard B Now if, after one quarter of those then in 0 was equally divided into three and each lot put into'yards A, B, and D, there would be the same number in eacli of the four enclosures, how many sheep were in each of the four yards before the drovers commenced to draft?

LAST WEEK’S SOLUTIONS. THE WAHINE AND THE MAORI. The Maori must have been six and twothird hours longer making the trip to Lyttelton than the Wahine travelling to Wellington, both leaving at the same time. DINING TOGETHER. There are 13 different ways that the married couples could be seated under the conditions stated. A HABERDASHERY SHOP. The respective quantities were 105, 35, 21, 15, 7,5, 3, and 1, the*prices being Is 2d, lid, 2id, 3id, 7id, 104 d, Is sid, and 4s 4J>d THE AIRPLANE SOUTHERN CROSS. The hop-off wss on Wednesday. A NOVEL FAMILY RECORD. The oldest tree must have been 20 years of age when the youngest child was born. ANSWER TO CORRESPONDENT. G. H. G.—lt will be found on page 39 of the book mentioned. A CORRECTION. The following-moves were inadvertently omitted last Tuesday from the solution of the “ Mings ” and “ Manchus ” problem:—2 to 1, 5 to 2, 3 to 5, 6 to 3, 7 to 6, 4 to 7, 1 to 4, 3 to 1 6 to 3, 7 to 6.