INTELLECT SHARPENERS

Otago Daily Times, Issue 21993, 30 June 1933, Page 2

INTELLECT SHARPENERS

Written for the Otago Daily Times. By T. L. Britoh. CROSSING A RIVER. A correspondent, “ Nelson M.,” has forwarded an interesting little puzzle of the “Crossing a river ” type which may give the reader 10 minutes, or perhaps longer, of mental enjoyment. It is a slight variation of the well-known “ Missionary-Can* hihal ” problem; the difference being that l i’u the latter puzzle it is ; stipulated : that only one' of the missionaries and one of the cannibals can row the boat, whereas in the one submitted by “Nelson M. three constables and one prisoner are so :capable. In the old-time puzzle thirteen crossings are required get the party across under conditions similar m_ every other respect to those imposed in the present problem, and it will be interesting to know whether the reader can make use of the prowess of the extra two constables, and get the six people over the stream in a smaller number of crossings. It taay be stated that the sender of the puzzle considers that fifteen crossings are necessary, his statement of the question being put in this way: Three eqnstables require to transport themselves and three prisoners; across a river by rowing boat which can hold only two persons at one time, ihe precautionary measures usual in such cases are taken for the proper supervision of their charges, the main one affecting the problem being that on no occasion does the number of prisoners exceed the number of constables present on any side of the river. They accomplish the feat in the smallest number of crossings possible, and the question is: Was that nuraher more dr less'.than the number , stated by the sender? It will, of course, be taken for granted that those crossing over must be in and not outside the boat, so that all trick methods such as using tow ropes are eliminated, the only means of , propelling the craft being rowing by one or two persons. TWO FOR THE ARMCHAIR. It took Jones exactly four hours to travel from A to B and back again by the same route without any perceptible stop. The outgoing journey was a puU all the way, although the grade, of , one in forty is only a slight one, but it ma.de a considerable difference on # his return walk, for that was travelled in one-third of the time occupied on the outward journey. The question arising from these few details is: How far is it from A to B if the second half of the distance was covered at the rate of three miles an hour? , . , • I have just written down two separate numbers, each of them being less a century. When the smaller of these two numbers is subtracted from the other the result is exactly fifty less than when they are added together. Another feature is that if the two results of the subtraction and addition processes referred to are added together the total is greater by seventy-nine than the smaller of the two numbers written down. If the would-be solver of this innocent little question will read it carefully, he will note that one clause of the statement gives the clue to the identity of the two numbers in question, there being only two different digits in both. What are they? RENTING 'A HOUSE. Requests are not infrequently received from readers for an occasional anthmeti* cal puzzle involving a calculation or an everyday business character. Here is one concerning the renting of a house that should come well within the category mentioned, apd is,not by- any, means difficulty A gentleman took- a lease o{ _ a house for a term of three years from the first day of January last, the rental of which is £2OO per annum, payable under the conditions.of the contract at the end of each year. ' He decided, however, with the consent of the owner of the house, to pay down on the day that the lease com* menced a certain sum of money which would be sufficient to reduce his annual rental payments to '£l2o instead of the fixed rental of £2OO, hs, per contract, the payment being accepted and the terms; of lease varied accordingly. The question for the reader who enjoys this class of puzzle is, How much did the gentleman pay down in the way mentioned, so that the payment >of £BO less, per annum would be equivalent to the rental fixed by the lease? Compound interest may be reckoned at the rate of 4 per cent, per annum, and to simplify the calculation the required sum may be stated in an,even number of pounds, fractions (if any), being ignored.

FIVE PADDOCKS. X “ Rural ” has sent a problem, : which though of Stone Ace antiquity,.still provides material, for a good measure of controversial discussion, for which reason it is published. A farmer has t a large block of land of rectangular shape, 60 chains by 20, which he subdivided 'into five paddocks, all oblong in shape* xhe whole area was first divided into two equal parts by a fence running from one short side to the other ._ _ The top, or northern half, was then divided into three paddocks, each 20 chains by 10, and the southern part into two paddocks, each 30 chains by 10, the 120 acres being thus subdivided into five paddocks. _ Besides the nine gates that lead. outside from each of the five paddocks, the corner blocks each having two, there are seven other gates leading from one paddock to another, so that there are four gates in the line of fencing which first divided the; whole block into two equal parts. The puzzle may perhaps be stated in the words of the sender: "The, farmer has trained his dog to go alone through the five paddocks to start up« * cast ~ sheep, and bounding off from the homestead at the master’s call, the dog entfere all paddocks by jumping over, once only, every one of the 16 locked gates without once crossing his track. The gate which the dog ‘clears* by jumping out of the lastvisited paddock to return to the homestead is the only one jumped twice.” The correspondent wishes to know what route the dog follows? " Rural ” adds that he has not been an eye-witness of the performance of this wonderful dog, but knows that he performs the feat. Has the reader any comments to make on the latter statement or upon the question generally?

TWO SIMPLE. “RESTORATIONS.” Here are two “restoration” puzzles which, though not difficult, should give the ingenious reader some mental enjoyment and exercise. Four figures are in the multiplicand of a multiplication sum, three of which are missing, and the other being a four in the third position reading from the left. The unit digit of the two-figure multiplier is also missing, the other figure being a five. Everyone of ■the five figures of the first line .of multiplication when five is the multiplier, is not available to the would-be solver, the'secqnd multiplied line being 2 3 x x 7. in which the x denotes an .absent digit. The result is 4 x 0 x 9 x. . . ; The other sum is one of division, where the calculation is made by two factors of a divisor of two figures. The dividend in the first short-division sum is one of five figures, all of which are missing, and the result is 8 I x 1 with 2 over. The next division by the other factor does not reveal any particulars except that there is a 3 over. I_ wonder if the reader can reconstruct this little sum with only the above data. If not. perhaps if he knows that had the . sum been one of long division the remainder would, be 23 he. should have no .'difficulty. With_ it. But he will get more intellectual enjoy-, ment from the effort to find the solution without using the information given in the last sentence, for the data are sufficient without it. SOLUTION OE LAST WEEK’S PROBLEMS. A TRINKET BOX The four pieces should be each one inch square. , TRAIN SPEEDS, The second train travelled at the rate of 22 J m.p.h., the other being 474 feet long. ; SALARY INCREASES. The respective salaries for 1932 were £llOO and £960, the rate of increase in Brown’s case being 20 pet cent, in each of the years 1931 and 1932. THREE FOR THE ARMCHAIR. (1) Sixteen inches by twelve. (2) Twenty-eight and four-fifths minutes in 12 hours true time. (3) Teh per cent, of the amount of income for the period mentioned would be £7.

answers to correspondents. “ Metric.” —(1) The unit is the metre, and divided into 100 equal parts the centimetre represents one of them. (2) The system was used by the Allies during the Great War, being much simpler than our own. (3) The decimal referred to does not terminate. J. H. C. —It is much too technical for this column, but has been placed on file for use if required. Much obliged for appreciation. “ Inquirer.”—Next week.

FROM FIVE REGIMENTS. The arrangement was as follows:— A S. B R. C G. D L. E P. CL. DP. E S. A R, B G. E R. A G. B L. CP. D S. B P. C S. D R. E G. A L. D G. EL. A P. B S. C R.