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'More Old Chestnuts' printed from http://nrich.maths.org/

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This is the second in a sequence of three articles, and follows on from Old Chestnuts

In preparing the talk "Let's look forwards by glancing back" I had been keen to include a problem that had beset me during my adolescence. I vaguely remembered it was from Durrell. But in those schoolboy days mathematics was Durrell, first and last. It was only later that Porter, Quadling and Ramsey would take over hours of my youth.

After some searching I had unearthed the book and found the very question that all those years ago my father and I had agonised over. My memory may have been playing tricks but I found myself reconstructing my original points of view and then his.

At the time father was right and I was wrong. See how you get on:

Dreams of Durrell

Bath time

A bath has two taps A, B and an outlet C. With A turned on, it fills in 15 minutes; with A and B turned on, it will fills in 10 min. ; with B turned on and C opened, the water-level remains stationary.

How long will it take to fill the bath with A turned on and C opened?


Another practice from my early schooldays had been that whenever a lesson ended early, revision of long multiplication and division was the order of the day.

Calculators had not been dreamed of and those early fumblings with a slide rule did little to reassure. Especially when accuracy was required.

So, at the first lull in the talk the following was put on the OHP:

Just for old time's sake!

Multiply

82164973 by 3037

Divide:

62015735 by 7803


How did you get on? Sorry, no answers at the end of this article.

About half way through the talk consideration was given to how successive mathematics curricula were arrived at. During much of the twentieth century, school mathematics was believed to have been socially and culturally underpinned.

How does yesteryear compare with today?

Nowadays, many cynics believe that political considerations and financial restraints are the limiting factors of expedience.

Whatever, the audience was asked to consider what sort of social conditions might have prevailed when Alligation was done regularly in our schools:

Alligation

Medial alligation

A grocer mingled 4 cwt. of sugar at 56s. per cwt., 7cwt. at 43s. per cwt. and 5 cwt. at 37s. per cwt.

I demand the price of 2 cwt. of this mixture

Alternate alligation

Alternate alligation

A grocer would mix raisons of the sun at 7d. per lb. with Malagas at 6d. and Smyrnas at 4d. per lb.

I desire to know what quantity of each sort he must take to sell them 5d. per lb.?

Perhaps there is a need to remind many of you of the measures in existence then:

12d to the shilling (s). (12 old pennies)
20s to the pound (£).

112 lb (pounds) to the hundredweight (cwt)!
20 cwt to the ton.

Some aspects of numeracy, (perhaps best forgotten! )are included in the next article