“Stump the Chump!:” Solve These Puzzlers from 1748

This is for all our readers who have been thinking that there really ought to be a post about math and science once in a while.

Yesterday I was looking at the three editions of Arithmetic Made Familiar and Easy to Young Gentlemen and Ladies, the second volume in The Circle of Sciences published by the famous 18th-century English children’s book publisher, John Newbery.  The Circle was designed as a set of books that was supposed to give young Britons everything necessary for successful careers in business and for the fulfillment of their civic duties.  John Locke considered chronology, geography, grammar, handwriting, logic, poetry, and rhetoric essential and all these subjects were covered in The Circle.

Like all the volumes in the set, Arithmetic Made Familiar and Easy is written in the form of a catechism, or a series of questions and answers.  Although this sounds as dry as dust to us, the catechism was considered a kind of conversation and conversation trumped lecture in eighteenth-century educational theory as a lively way of presenting a body of information.

The Circle of Sciences remained in print for decades, probably because the volume editors made genuine attempts to engage young readers.  The editor of Arithmetic Made Familiar and Easy went to some trouble to give his readers more than tables and huge horrible sums, as the Church Mice called them.  There’s a description of an abacus.   Changing ringing is used as an example of a arithmetical progression and thank heavens it’s shorter than Lord Peter Whimsey’s calculations in Dorothy Sayers’s The Nine Taylors…  To show how to total an invoice, the editor drews up a bill of the sort school boys were presented for purchases of apples, gingerbread, marbles, and oranges.  A multiplication problem showed how to figure out the costs of x number of yards of lace so a fashionable miss could check her tradesman’s bill for mistakes or overcharges.

There are also witty word problems.   Our first puzzler from Arithmetic Made Familiar is in verse and it seems to have been a golden oldie.  It had been circulating at least since 1708, where it appeared as an example of “vulgar arithmetic” in The Ladies Diary or Womens Almanack.

When first the Marriage-Knot was ty’d

Betwixt my Wife and me,

My Age did hers as far exceed

As three times three does three:

But after ten and half ten Years

We Man and Wife had been,

Her Age came up as near to mine,

As eight is to sixteen.

Got that?   Now try our second puzzler:

A Man overtaking a Maid who was driving a Flock of Geese, said to her, Good-morrow, Sweetheart, whether are you going with your 99 Geese?  Sir, said she, you mistake the Number; for if I had as many more, and half as many more and one fourth Part as many, then I should have but 99.  The Question is, how many Geese she had?

Readers are invited to submit solutions to one or both of the puzzlers in the comments. Staff members of Car Talk, you are ineligible to enter this competition! The answers will be posted next week.




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