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## Greetings from England!

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**Greetings from England!**Dr Geoff Tennant g.d.tennant@reading.ac.uk**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**So here’s the problem!**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!**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 bless you always Dr Geoff Tennant Institute of Education, University of Reading, UK Visiting lecturer at the University of West Indies until March 23rd g.d.tennant@reading.ac.uk**So here’s the problem (1)!**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 (2)!**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!**OK, so you know that problem (1)**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 (2)**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?**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!