NUTS TO CRACK

Otago Witness, Issue 4031, 16 June 1931, Page 7

NUTS TO CRACK

By

T. L. Briton.

(Fob the Otago Witness.) Readers with a little ingenuity will find In this column an abundant store of entertainment and amusement, and the solring of the problems should proride excellent mental exhilaration. While some of th. " 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 comparison with those published in the issue following the publication of the problems ANOTHER CODE. Correspondence from readers indicates that an occasional mystery puzzle, such for instance as a cryptograph, is appreciated, and the tenor of the comment upon the-subject suggests a somewhat romantic side to these interesting probblems. Apart from the implied challenge to one’s intellect, it reveals a universal weakness for things occult, and the 'very human desire to discover a secret in whatever guise it may appear. In this cryptograph the idea adopted is new, so far as the writer is aware, but it will perhaps be sufficient for the would-be solver to know that the words are formed by a uniform transposition of letters, and if it is further stated that some of the letters used are not essential, being without orthographical value, it is to be hoped that the secret has not been entirely given away. XEMHQT MTRXA MFO RIEXHMT NOXITCQURTMSNXOC, ELMBIGJILMLETNJI MOT XESOJHXT MOHXW QWOMNK XEMHOT JYEXK, XDNQA MESQIWRXEHJTO MOT XESOJHXT MOHXW OMD QTXON, JSAXII NEEJXB MQDEIDXUTMS ROXF SEIRQUTXNEMLC, XDNQA GNXIRQUD RAXW ROM NOILXQLEJBERM RIEXHJT TXCERJROXC NOIXTATJERPXRETMNIZ MSXf MFO XTAJERZG ECXIVQREMS MOT XEMHQT METISXOPQMPOJ MEDXJISZ XFMI DMEXREQVMOCSXID.

WITH TEN COUNTERS. . Here is a little arithmetical problem that should test the ingenuity of the reader and at the same time provide him with an interesting game of solitaire. Take the nine digits 1 to 9, and the cipher 0, and place them in form of a circle in the following order, reading in the direction that the hands of a timepiece move—6, 3,2, 8,9, 0 7,1, 5, 4. The problem is to divide these 10 counters into three groups so that the number represented by one of them multiplied by that of another will make a product as indicated by the number in the third group, the figures when forming the groups to be retained in the order given. An example of grouping i 5—71—546—32890, but in that case the arithmetical part of the puzzle does not conform with the conditions laid down. There is no mathematical rule nor any formula by which the arrangement maybe discovered, and for that reason alone the problem -will no doubt provide the reader with half an hour of mental recreation. A SIMPLE GEOMETRICAL PUZZLE. What is the largest number of parts into which a circle, say in the form of a circular piece of paper, may be divided with six straight complete cuts of a scissors or other suitable instrument, it being immaterial of course what size the circle is? This problem may be better solved by a diagram, and the use of a pencil instead of a cutting instrument will not invoke the wrath of the maid when cleaning the room next day, but in any case the question assumes “cuts” will be made through the whole circle and the pieces not moved or piled. If, therefore, the reader will draw six straight lines through the circle in the proper way so that they will show the maximum number of divisions, it may surprise him to find what a large number of separate pieces (should the ' “ cutting ” process be adopted) into which the circular papei can be divided by merely making this number of straight complete cuts oi lines. Can the reader find what ths maximum number is? There is a sirnph formula for problems of this kind whicl will be published with the solution.

IN A NINE-SQUARE. Whilst the reader is in the vein, here is another little problem to test his ingenuity more than his mathematical skill, but it is more of the armchair variety than the previous one. Number nine counters 1 to 9 respectively, and place one in each of the cells in a nine square, so that the three-figure number in the bottom row equals three times that in the top row and the latter number exactly one-half of the number shown in.. the middle row. Here is one example:— 3 2 7 6 5 4 9 8 1 Can the reader find any others in which the top and middle rows are equivalent to one-third and two-thirds respectively of the bottom row? UP AND DOWN HILL. The simplest questions, particularly those involving figures, are very often apt to trip the unwary and sometimes others who are constantly on the “ look-

out ” for pitfalls are caught by the most innocent-looking problems. There is no trap in this one, though possibly it may necessitate the would-be solver donning his thinking-cap. I took the mountain road from a certain point to walk up to the rest house 3000 feet above sealevel, and during the ascent averaged a rate of walking of one mile and a-half per hour. When I was coming down by the same track to the starting point my average walking speed was three times as much as on the upward journey. The simple little question is, How far is it from the starting point to the rest house by the route taken if the time occupied there and back was exactly six hours? For problem purposes it may be assumed that there was no perceptible delay between the time of arrival at and the departure from the mountain resort mentioned. SOLUTIONS OF LAST WEEK’S PROBLEMS. A CRYPTOGRAPH. The heavy decrease in Moslem pilgrimages to Mecca, one result of the worldwide depression, is affecting the Hedjaz revenues. King Ibn Saud has therefore ordered propaganda by films to show the wonders of \ Mecca, including the Prophet’s grave to attract the faithful from all parts of the world. MEASURING THREE GALLONS.' Eight minutes fifteen seconds for 11 operations. SIX PENS. Sixteen is the fewest number possible under the conditions, and they are:— D. C. B. D. C. E. A. B. D. C. E. D B. A. D. E. A MUTILATED NUMBER PLATE. 9801.

AN UNEXPECTED HAPPENING. As the terms of the will implied that a son was to receive twice as much as the mother, and the latter twice that of a daughter, the former should get foursevenths, the mother two-sevenths, and the other twin one-seventh. ANSWERS TO CORRESPONDENTS. “ Rule.”—There are several points involved. First, one of the' two numbers mentioned must be at the &nd of the second row, though that was not stipulated. Second, the remaining part is confined entirely to the squares. The other points should now be obvious. Thanks for comments. “ H. C.”—Merely a matter of finding the - smallest number.