III.

DINAH MITE. JANET. MAGPIE. TAFFY.

ANSWERS TO KNOT X.

§ 1. THE CHELSEA PENSIONERS.

_Problem._--If 70 per cent. have lost an eye, 75 per cent. an ear, 80 per cent. an arm, 85 per cent. a leg: what percentage, _at least_, must have lost all four?

_Answer._--Ten.

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_Solution._--(I adopt that of POLAR STAR, as being better than my own). Adding the wounds together, we get 70 + 75 + 80 + 85 = 310, among 100 men; which gives 3 to each, and 4 to 10 men. Therefore the least percentage is 10.

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Nineteen answers have been received. One is "5," but, as no working is given with it, it must, in accordance with the rule, remain "a deed without a name." JANET makes it "35 and 7/10ths." I am sorry she has misunderstood the question, and has supposed that those who had lost an ear were 75 per cent. _of those who had lost an eye_; and so on. Of course, on this supposition, the percentages must all be multiplied together. This she has done correctly, but I can give her no honours, as I do not think the question will fairly bear her interpretation, THREE SCORE AND TEN makes it "19 and 3/8ths." Her solution has given me--I will not say "many anxious days and sleepless nights," for I wish to be strictly truthful, but--some trouble in making any sense at all of it. She makes the number of "pensioners wounded once" to be 310 ("per cent.," I suppose!): dividing by 4, she gets 77 and a half as "average percentage:" again dividing by 4, she gets 19 and 3/8ths as "percentage wounded four times." Does she suppose wounds of different kinds to "absorb" each other, so to speak? Then, no doubt, the _data_ are equivalent to 77 pensioners with one wound each, and a half-pensioner with a half-wound. And does she then suppose these concentrated wounds to be _transferable_, so that 3/4ths of these unfortunates can obtain perfect health by handing over their wounds to the remaining 1/4th? Granting these suppositions, her answer is right; or rather, _if_ the question had been "A road is covered with one inch of gravel, along 77 and a half per cent. of it. How much of it could be covered 4 inches deep with the same material?" her answer _would_ have been right. But alas, that _wasn't_ the question! DELTA makes some most amazing assumptions: "let every one who has not lost an eye have lost an ear," "let every one who has not lost both eyes and ears have lost an arm." Her ideas of a battle-field are grim indeed. Fancy a warrior who would continue fighting after losing both eyes, both ears, and both arms! This is a case which she (or "it?") evidently considers _possible_.

Next come eight writers who have made the unwarrantable assumption that, because 70 per cent. have lost an eye, _therefore_ 30 per cent. have _not_ lost one, so that they have _both_ eyes. This is illogical. If you give me a bag containing 100 sovereigns, and if in an hour I come to you (my face _not_ beaming with gratitude nearly so much as when I received the bag) to say "I am sorry to tell you that 70 of these sovereigns are bad," do I thereby guarantee the other 30 to be good? Perhaps I have not tested them yet. The sides of this illogical octagon are as follows, in alphabetical order:--ALGERNON BRAY, DINAH MITE, G. S. C., JANE E., J. D. W., MAGPIE (who makes the delightful remark "therefore 90 per cent. have two of something," recalling to one's memory that fortunate monarch, with whom Xerxes was so much pleased that "he gave him ten of everything!"), S. S. G., and TOKIO.

BRADSHAW OF THE FUTURE and T. R. do the question in a piecemeal fashion--on the principle that the 70 per cent. and the 75 per cent., though commenced at opposite ends of the 100, must overlap by _at least_ 45 per cent.; and so on. This is quite correct working, but not, I think, quite the best way of doing it.

The other five competitors will, I hope, feel themselves sufficiently glorified by being placed in the first class, without my composing a Triumphal Ode for each!

CLASS LIST.

OLD CAT. OLD HEN. POLAR STAR. SIMPLE SUSAN. WHITE SUGAR.

BRADSHAW OF THE FUTURE. T. R.