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114 "Patience") before any solution would have been hit on by the most ingenious of them.

Forty-five answers have come in, of which 44 give, I am happy to say, some sort of working, and therefore deserve to be mentioned by name, and to have their virtues, or vices as the case may be, discussed. Thirteen have made assumptions to which they have no right, and so cannot figure in the Class-list, even though, in 10 of the 12 cases, the answer is right. Of the remaining 28, no less than 26 have sent in accidental solutions, and therefore fall short of the highest honours.

I will now discuss individual cases, taking the worst first, as my custom is.

gives no working—at least this is all he gives: after stating the given equations, he says "therefore the difference, 1 sandwich + 3 biscuits, = 3d.": then follow the amounts of the unknown bills, with no further hint as to how he got them. has had a very narrow escape of not being named at all!

Of those who are wrong, has sent in a piece of incorrect working. Peruse the horrid details, and shudder! She takes $$\scriptstyle x$$ (call it "$$\scriptstyle y$$") as the cost of a sandwich, and concludes (rightly enough) that a biscuit will cost $$\scriptstyle \frac{3\ -\ y}{3}$$. She then subtracts the second equation from the first, and deduces $$\scriptstyle 3y\ +\ 7\ \times\ \frac{3\ -\ y}{3}\ - 4y\ +\ 10\ \times\ \frac{3\ -\ y}{3}\ =\ 3$$.