Part 16 (1/2)

Next come eight writers who have made the unwarrantable a.s.sumption 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 grat.i.tude 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 fas.h.i.+on--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 compet.i.tors will, I hope, feel themselves sufficiently glorified by being placed in the first cla.s.s, without my composing a Triumphal Ode for each!

CLa.s.s LIST.

I.

OLD CAT.

OLD HEN.

POLAR STAR.

SIMPLE SUSAN.

WHITE SUGAR.

II.

BRADSHAW OF THE FUTURE.

T. R.

III.

ALGERNON BRAY.

DINAH MITE.

G. S. C.

JANE E.

J. D. W.

MAGPIE.

S. S. G.

TOKIO.

-- 2. CHANGE OF DAY.

I must postpone, _sine die_, the geographical problem--partly because I have not yet received the statistics I am hoping for, and partly because I am myself so entirely puzzled by it; and when an examiner is himself dimly hovering between a second cla.s.s and a third how is he to decide the position of others?

-- 3. THE SONS' AGES.

_Problem._--”At first, two of the ages are together equal to the third.

A few years afterwards, two of them are together double of the third.

When the number of years since the first occasion is two-thirds of the sum of the ages on that occasion, one age is 21. What are the other two?

_Answer._--”15 and 18.”

_Solution._--Let the ages at first be _x_, _y_, (_x_ + _y_). Now, if _a_ + _b_ = 2_c_, then (_a_-_n_) + (_b_-_n_) = 2(_c_-_n_), whatever be the value of _n_. Hence the second relations.h.i.+p, if _ever_ true, was _always_ true. Hence it was true at first. But it cannot be true that _x_ and _y_ are together double of (_x_ + _y_). Hence it must be true of (_x_ + _y_), together with _x_ or _y_; and it does not matter which we take. We a.s.sume, then, (_x_ + _y_) + _x_ = 2_y_; _i.e._ _y_ = 2_x_.