NUTS TO CRACK

Otago Witness, Issue 3993, 23 September 1930, Page 20

NUTS TO CRACK

By

T. L. Briton.

(For the Otago Witness.)

Readers with a little ingenuity will find in this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental »exhilarat!on. 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 tn our next Issue, together with some fresh “ nuts." Readers are requested not ■to send tn 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. THE FREE AMBULANCE. Seeing the'sale of art-union tickets in aid of that excellent institution the free ambulance, four visitors after each purchasing a book, decided to subscribe in equal shares, a joint donation to the funds, agreeing upon the total sum to be sent. Upon counting the cash that each had with him, F found that he had exactly one-third more than the amount of each share, U was six shillings and eightpence short of his, N had ’ only half of his quota, while D had exactly, twice the amount of each contribution. F, U and N then gave their money to D, the four sums totalling £4 14s lOd, which was in excess of the amount agreed to be given. Now if the aggregate sum mentioned was in excess of the total contribution, by four pence more than the sum one of the party had with him at the time, what was the total subscription donated by these four generous visitors, F, U, N, 15? “SANS” FIGURES. A correspondent, “ Best Friend,” writes:—“X had no brothers or sisters, but Y was a near relative, inasmuch that the mother of X was the mother-in-law of Y’s mother. How were the two related ?” Perhaps the reader can enlighten the questioner. Whilst in this vein here is a curious statement that has been argued and discussed on occasions without end and is still a subject of controversy. Is it possible in New Zealand, or was it ever possible under the law, for a man to have married his WIDOW’S sister? The word has been written in capitals by way of indicating that there is no confusion in the mind of the writer of these notes, with the term “ Deceased wife’s sister.” A simple “ Yes ” or “No ” is hardly sufficient without an explanation, which will be given next Saturday. In the meantime perhaps the reader will ponder over it. ( POSSIBLY DIFFERENT. Here is a little puzzle that may possibly in some respects be different to any that the reader has had before him. though it may npt be wholly new, especially to experts in “ magic square ” problems. Take seven strips of paper and write on each the figures 1,2, 3,4, 5,6, 7, in that order. The problem is to place the 49 numbers in a seven by seven square, so that the seven perpendiculars, the seven horizontals, and the two long diagonals will each add up the same. Of course, if the figures were separate, it would be easy of solution, but the reader is permitted to cut the strips of paper into as many single pieces as desired, the successful solver being the one who accomplishes the feat in the fewest number of “cuts.” Mr Ernest Dudeney is the author of this entertaining little poser, and perhaps our “ magic square ” devotees may like to comment upon it. FIXING THE SIZE. The reader having his pencil at hand after solving the last problem, let him make a diagram of a four-sided figure, with its sides four, three, six, and five inches respectively. It will be observed that such a figure under these or similar conditions could be of various sizes according to shape, even though the sides be perfectly straight as in the present case. But if we mark a point within the figure an equal distance from each corner, it can be of only one size. What is the area of the figure in the diagram just drawn? There is a simple little rule for this which is useful to know, and will appear with the solution next week. A SURPLUS. This has no reference to State finance though it concerns a commodity that is an important factor in producing a Budget surplus. An empty room in a large freezing works measures in length 12ft, width 10ft, and Bft in height, with no posts or other obstacles to prevent maximum storage. The workmen had just finished stacking to its capacity, a number vf boxes of butter, when the overseer gave instructions, to place oneinch battens under each layer. This having been completed, there was, of course, a surplus of quite a quantity of butter which could not be re-stored, and if the boxes were of uniform size, viz., each side 96 square inches, each end 80, and top and bottom each 120 square inches, what was the surplus after repacking? LAST WEEK’S SOLUTIONS. ON THE BRIDGE. At the respective rates of steaming (alI lowing for the wind) of 20 and 12 k.p.h., I the vessels must have passed one another at half-past 1 a.m.

TRAVELLING PARALLELLY. 18.18 miles per hour. 2846 yards. ONE FOR THE ARMCHAIR. Twenty-four miles, four and a-halfi miles per hour being the par rate. A COURT’S JUDGMENT. The variation of the will made a differ-x ciice of £205 2s 6d to the widow of the testator. DIFFERENT WAYS HOME. One hundred and seventy-eight three-quarter yards. ANSWERS TO CORRESPONDENTS. J. B. D.—Thanks for interesting comments. R. A. Proctor was an accepted authority in mathematics, and the article in Knowledge was an extract from an early astronomical work. “ Curious.”—(l) Only through this column. (2) It applies to the one instance only. R. P.—The same number could be sq placed that the enclosure would not be large enough for one, though iq another shape its maximum capacity would be 100. “ Moutere.” —(1) The solution is limited to the expressed terms of the prob-: lem, thus any “ pouring ” must be confined to the seven and eight. (2) Total of combined ages omitted. (3) Yes, there are other squares. H. J. B.—Thanks. G. M‘D. —Explained in the Otago Daily Times, June 8, 1929, which, no doubt, you will be able to refer to. ON THE BRIDGE. A whole line was omitted in stating this problem last Saturday, “ viz., fixing the distance at 200 miles.”