Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 20988, 26 September 1931, Page 5 (Supplement)

Intellect Sharpeners.

" RESTORATION » PROBLEM. BY T. L. BRITON. ' Here is an arithmetical puzzle that will demand as much patience and ingenuity as the decoding of an obscure cryptograph, namely, to restore the figures of a completed sum in which.most of the digits have been deleted. It is-a sum in long division and can correctly be written down from the following description. All these figures in the divisor are missing, as well as six digits from the dividend, the only available figure being the last one which is a " foux*," and of the four figures that form the full quotient, only one of them can be identified, tiiis being the second one which is also a " four." After the divisor has been multiplied by the first figure of the quotient, and the three-figured product subtracted it reads, xx4x, including the figure brought down, the x represents a deleted digit. The divisor multiplied bv four is xxxx,''the result of the subtraction being also xxxx, but when the third multiplication is made the product is x4x. All subsequent figures are missing, and the sum works out evenly without a remainder. Can the reader restore these ? ANTICIPATING THE "CUT." Exactly 18 months ago Jones anticipated the " cut " in salaries, and from that time he used the pruning knife on household and personal expenditure and for the whole of that period kept correct details of income and disbursements, which form the basis of this problem. During that time three-sevenths of his annual income had gone in rent, rates and I taxes, two-fifths of it in ordinary household expenses including his wife's " pinmoney " and one-seventh of it was spent in travelling and personal expenses. It thus enabled him to meet the "historical" taxation that the Minister of Finance has imposed, but that is not the point of the problem. The question is, if his new banking account covering this period only included the \*hole of his salary and all items of expenditure, resulting in a credit balance of exactly £lB5, can the reader find what was the annual salary received ? IN SILVER COINS. Although perhaps the- reader sought the aid of pen or pencil in reaching a satisfactory answer to the previous question, I here is one that may easily be answered I while he is sharpening his pencil for- the next. A visitor to a charity institution handed to the director a sum' of money sufficient to give to each inmate a certain amount to be paid in silver coins. The report of the incident did not mention' the actual sum to be given to each, but the genferous act suggests a problem on the subject of silver coins. Let it be assumed that the total sum handed to the director was £23 8s 9d and that each inmate received one silver coin of each denomination in New Zealand currency. Can reader find how many participated in the donation ? The arithmetic of this is absurdly simple if the would- . be solver knows the way to proceed and, of course, it is much more quickly done with pencil and paper. OBVERSE AND REVERSE. Here is another every-day question that should not take more than a few moments , to satisfactorily dispose of. I have six metal discs in the form of advertising tokens and similar in all respects to one another. On the reverse side is an imprint of a large warehouse and factory, while on the other side, the obverse, is the " Queen o£ Industry," representing in particular New Zealand's staple industries. The question is what are the I chances of these six discs when thrown i loose in the air at the same time, that I at least four of them will fall with their ' obverse sides uppermost, or the reverse j position ? Arithmetically this is on all fours with the question asked in the preceding problem, but it should be carefully read before tackling it. ' ' 9' MEXICAN DOLLARS AND CENTS. Here is a problem which has come from a reader, H.C.L., and is somewhat on the same lines as one which appeared a few months ago, though different in the method of reaching the result. The correspondent has evidently overlooked the fact that the fluctuating price of silver makes it impossible to fix the number of cents to the dollar of this currency, when paid in subsidiary coiifs, but for the purposes of the problem we will assume that one hundred is the fixed rate. A purchaser of an article to the value of 68 cents had only a two-dollar note, one six-cent and one four-cent piece. The dealer from whom the purchase was made could not give him the exact changej as he had only a one-dollar piece and one half-dollar. At that moment the dealer's wife came into the shop and she handed to her husband the contents of her purse consisting of two twenty-cents and one each of ten, four and two-cent pieces. By using the whole of these 10 different coins the dealer was able to complete the sale to the customer and return his wife's money, though not in the same coins. How was . it arranged so that no one had the sipie coins afterwards ? LAST WEEK'S SOLUTIONS. A Cipher.—We can maintain and even improve our standard of living if we intensify our efforts, but we shall never begin until we have restored the normal incentive to effort. (Eight letters had more than one equivalent each). Curious Conditions.—The distribution would have to cease after the seventh year, as seven is the maximum number of different ways the two classes could be made up to wholly exhaust the yeaily sum. Problem in " Exchange."—Twenty, three is the lowest number. Venture in Flax.—Tho speculator invested £1350 in the industry. Rejected Problem.—Tho couples were C and G; E and K; II and A. ANSWERS TO CORRESPONDENTS. !• Logarithms."—They simplify calculations, but space cannot be spared for an explanation of their use which enables operations of multiplication and division to bo reduced to little more than simple addition and subtraction. " Mystic.."—A number of readers have written in similar strain re cryptographs. Thanks for comment.