In the following Class-list, I hope the solitary occupant of III. will sheathe her claws when she hears how narrow an escape she has had of not being named at all. Her account of the process by which she got the answer is so meagre that, like the nursery tale of "Jack-a-Minory" (I trust I. E. A. will be merciful to the spelling), it is scarcely to be distinguished from "zero."
AYR. BRADSHAW OF THE FUTURE. F. LEE. H. VERNON.
_Problem 1._--_A_ and _B_ began the year with only 1,000_l._ a-piece. They borrowed nought; they stole nought. On the next New-Year's Day they had 60,000_l._ between them. How did they do it?
_Solution._--They went that day to the Bank of England. _A_ stood in front of it, while _B_ went round and stood behind it.
Two answers have been received, both worthy of much honour. ADDLEPATE makes them borrow "0" and steal "0," and uses both cyphers by putting them at the right-hand end of the 1,000_l._, thus producing 100,000_l._, which is well over the mark. But (or to express it in Latin) AT SPES INFRACTA has solved it even more ingeniously: with the first cypher she turns the "1" of the 1,000_l._ into a "9," and adds the result to the original sum, thus getting 10,000_l._: and in this, by means of the other "0," she turns the "1" into a "6," thus hitting the exact 60,000_l._
_Problem 2._--_L_ makes 5 scarves, while _M_ makes 2: _Z_ makes 4 while _L_ makes 3. Five scarves of _Z_'s weigh one of _L_'s; 5 of _M_'s weigh 3 of _Z_'s. One of _M_'s is as warm as 4 of _Z_'s: and one of _L_'s as warm as 3 of _M_'s. Which is best, giving equal weight in the result to rapidity of work, lightness, and warmth?
_Solution._--As to rapidity (other things being constant) _L_'s merit is to _M_'s in the ratio of 5 to 2: _Z_'s to _L_'s in the ratio of 4 to 3. In order to get one set of 3 numbers fulfilling these conditions, it is perhaps simplest to take the one that occurs _twice_ as unity, and reduce the others to fractions: this gives, for _L_, _M_, and _Z_, the marks 1, 2/5, 4/3. In estimating for _lightness_, we observe that the greater the weight, the less the merit, so that _Z_'s merit is to _L_'s as 5 to 1. Thus the marks for _lightness_ are 1/5, 5/3, 1. And similarly, the marks for warmth are 3, 1, 1/4. To get the total result, we must _multiply_ _L_'s 3 marks together, and do the same for _M_ and for _Z_. The final numbers are 1 × 1/5 × 3, 2/5 × 5/3 × 1, 4/3 × 1 × 1/4; _i.e._ 3/5, 2/3, 1/3; _i.e._ multiplying throughout by 15 (which will not alter the proportion), 9, 10, 5; showing the order of merit to be _M_, _L_, _Z_.