Our 'Conclusion', then, must be got out of the rather meager piece
of information that there is a red counter in the xy'-Square.
Hence our Conclusion is "some x are y' ", i.e. "some new Cakes are
not-nice (Cakes)": or, if you prefer to take y' as your Subject,
"some not-nice Cakes are new (Cakes)"; but the other looks neatest.

We will now write out the whole Syllogism, putting the symbol
&there4[*] for "therefore", and omitting "Cakes", for the sake of
brevity, at the end of each Proposition.

[*][NOTE from Brett: The use of "&there4" is a rather arbitrary
selection. There is no font available in general practice
which renders the "therefore" symbol correction (three dots in a
triangular formation). This can be done, however, in HTML, so if
this document is read in a browser, then the symbol will be properly
recognized. This is a poor man's excuse.]

"Some new Cakes are unwholesome;
No nice Cakes are unwholesome
&there4 Some new Cakes are not-nice."

And you have now worked out, successfully, your first 'SYLLOGISM'.
Permit me to congratulate you, and to express the hope that it is
but the beginning of a long and glorious series of similar victories!

We will work out one other Syllogism--a rather harder one than the
last--and then, I think, you may be safely left to play the Game
by yourself, or (better) with any friend whom you can find, that
is able and willing to take a share in the sport.