"This is queer," said McCrank to his friend. "Twopence added to twopence
is fourpence, and twopence multiplied by twopence is also fourpence." Of
course, he was wrong in thinking you can multiply money by money. The
multiplier must be regarded as an abstract number. It is true that two
feet multiplied by two feet will make four square feet. Similarly, two
pence multiplied by two pence will produce four square pence! And it
will perplex the reader to say what a "square penny" is. But we will
assume for the purposes of our puzzle that twopence multiplied by
twopence is fourpence. Now, what two amounts of money will produce the
next smallest possible result, the same in both cases, when added or
multiplied in this manner? The two amounts need not be alike, but they
must be those that can be paid in current coins of the realm.
The answer is 11/2d. and 3d. Added together they make 41/2d., and
11/2d. multiplied by 3 is also 41/2d.