© University of Reading 2007 www.reading.ac.uk

University of West Indies

April 21, 2023

Greetings from England!

Dr Geoff Tennantg.d.tennant@reading.ac.uk

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It’s cold in England right now…

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A sign we don’t get back home…

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Hurrah for her Majesty the Queen!

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Hurrah for Jamaican Independence!

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And hurrah for mathematics!

A problem I’d like to share with you…

Which is guaranteed to provoke a spontaneous gasp of awe and wonder!

You’ll need pen and paper….

….and I need a volunteer with a loud clear voice

Think of a three digit number, with the first and last digits different. So 123 would be fine but 121 isn’t

Reverse the digits – so 123 becomes 321

Subtract the smaller from the larger: in this case 321 – 123

If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075

Reverse the digits – so 075 becomes 570

Add the two last numbers together: in this case 075 + 570

Now can my volunteer open the envelope and read out the contents!

So here’s the problem!

A competition with a (very) smallprize per year group

Why does this always happen?

Note: full solution is hard, very interested in responses like, “What I noticed is that after the subtraction the numbers always……”

Email me at g.d.tennant@reading.ac.uk

If I have a lot of responses I’ll ask the Principal to invite me back!

Mathematics: a great subject to study…

-Intrinsically interesting, with beautiful connections eg. between algebra and geometry;

-Useful in everyday life – numeracy, problem-solving techniques;

-Underpins many lines of work – engineering, business, accountancy, science, actuarial science, ICT, meterology, economics, teaching, many others.

See http://www.mathscareers.org.uk/ for more information.

A special thank you…

…to all the mathematics teachers;

…and to all the teachers here.

May God bless you:

-Here at Holy Childhood School;

-As you leave and enter the adult world.

Thank you for having me…

May God blessyou always

Dr Geoff TennantInstitute of Education, University of Reading, UK

Visiting lecturer at the University of West Indies until March 23rd

g.d.tennant@reading.ac.uk

Think of a three digit number, with the first and last digits different. So 123 would be fine but 121 isn’t

Reverse the digits – so 123 becomes 321

Subtract the smaller from the larger: in this case 321 – 123

If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075

So here’s the problem (1)!

If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075

Reverse the digits – so 075 becomes 570

Add the two last numbers together: in this case 075 + 570

Now can my volunteer open the envelope and read out the contents!

So here’s the problem (2)!

Let’s try this – the counterfeit coin problem.

I have 9 coins that look and feel identical. One is lighter than the other 8.

I can use a weighing scale to balance coins against each other, but I have limited access, so need to use it as few times as possible.

How many uses of the

OK, so you know that problem (1)

How many uses of the weighing scales do I need to identify the one counterfeit coin?

What is the maximum number of coins from which I can identify one counterfeit lighter coin from with 3 uses of the balance? 4? 5?

Challenge (very difficult!) How do you identify one counterfeit coin, which may be either lighter or heavier, with 3 uses of the scales with 12 coins altogether?

OK, so you know that problem (2)

A competition with a (very) small prize per year group

Email me at

g.d.tennant@reading.ac.uk

with any solutions you have to any of these problems. I promise to reply to all emails.

If I have a lot of responses I’ll ask the Principal to invite me back!