Put down any number of pounds not more than twelve, any number of shillings under twenty, and any number of pence under twelve. Under the pounds put the number of pence, under the shillings the number of shillings, and under the pence the number of pounds, thus reversing the line.

Subtract.
Reverse the line again.
Add.

Answer, £12 18s. 11d., whatever numbers may have been selected.

Begin at the `1' in each line and it will be the same order of figures as the magic number up to six times that number, while seven times the magic number results in a row of 9's.

1. Introductory

AT a Lawn Tennis Tournament, where I chanced, some while ago, to be a spectator, the present method of assigning prizes was brought to my notice by the lamentations of one of the Players, who had been beaten (and had thus lost all chance of a prize) early in the contest, and who had had the mortification of seeing the 2nd prize carried off by a Player whom he knew to be quite inferior to himself. The results of the investigations, which I was led to make, I propose to lay before the reader under the following four headings --

(a) A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning.

(b) A proof that the present method of scoring in matches is constantly liable to lead to unjust results.

(c) A system of rules for conducting Tournaments, which, while requiring even less time than the present system, shall secure equitable results.

(d) An equitable system for scoring in matches.

2. A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning.

Let us take, as an example of the present method, a Tournament of 32 competitors with 4 prizes.

On the 1st day, these contend in 16 pairs: on the 2nd day, the 16 Winners contend in 8 pairs, the Losers being excluded from further competition: on the 3rd day, the 8 Winners contend in 4 pairs: on the 4th day, the 4 Winners (who are now known to be the 4 Prize-Men) contend in 2 pairs; and on the 5th day, the 2 Winners contend together to decide which is to take the 1st prize and which the 2nd -- the two Losers having no further contest, as the 3rd and 4th prizes are of equal value.

Now, if we divide the list of competitors, arranged in the order in which they are paired, into 4 sections, we may see that all that this method really does is to ascertain who is best in each section, then who is best in each half of the list, and then who is best of all. The best of all (and this is the only equitable result arrived at) wins the 1st prize: the best in the other half of the list wins the 2nd: and the best men in the two sections not yet represented by a champion win the other two prizes. If the Players had chanced to be paired in the order of merit, the 17th best Player would necessarily carry off the 2nd prize, and the