INTELLECT SHARPENERS

Otago Daily Times, Issue 21360, 13 June 1931, Page 20

INTELLECT SHARPENERS

Written for the Otago Daily Times. •By T. L. Briton. \ : ANOTHER CODE. i 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 MFC RIEXHMT XOXITCQURTMSNXOC, ELMBIGJILMLBTNJI MOT XESOJHXT MOHXW QWOMNK XEMHOT JYEXK, XDNQA MBSQIWRXEHJTO MOT XESOJHXT MOHXW OMD QTXOX, JSAXH NEEJXB MQDEIDXUTMS ROXF SEIRQUTXNEMO, XDNQA, GNXIRQUD RAXW ROM NOILXQLEJBERM • RIEXHJT TXCERJROXC NOIXTATJERPXRETMNIZ MSXI 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’ splitaire. Take the. nine digits 1 to 9, and the cipher 0, and place them in form of a circle in . the 1 following order, reading in the direction that the hands of a timepiece move—6, 3,2, 8,9, 07,1,5, 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 is— 7 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 may be discovered, and for that reason alone the problem will no doubt provide the reader with half an hour of mental recreation. / 1 v A SIMPLE GEOMETRICAL PUZZLE. What is the largest number of parts into which a circle, say in the form dfia circular piece of papgr, 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 that the “ 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 paper can he divided by merely making this 'number of straight complete cuts or lines. Can the reader find what the maximum number is? There is a simple formula foy problems, of this kind which 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 oqe in each of the cells in a nine square, so that the three-figure number in the bqttom 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:— 1 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 “ lookout ” 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 b.v 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. G. 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 1 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 end 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.