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Odds from evens up to 2020

Wednesday 1st January 2020

Welcome to 2020. I have been talking about this year for a long time. Ten years ago, when my job involved producing a long term technology development plan for the next ten years the report we produced was called 2020 Vision. Do you see what we did there?

Twenty Twenty

So now it is time for me to demonstrate some 2020 vision. In fact better than that I will try to see what the answer to my next question will be without you giving me any clues.

Think ahead to your birthday this year. How old will you be on that day? Add to that the two-digit version of the year in which you were born. With my 2020 vision I can already see that the answer you will get is 120. I knew that you would be impressed! Try this with your pupils but you will get an answer different than 120.

Now it is time for the puzzle of the month: If the sum of the positive odd integers less than 2020 is subtracted from the sum of the positive even numbers less than 2020 what is the result?

While we are thinking about 2020, did your realise that the first digit is the number of noughts in the number, the second the number of ones, the third the number of twos and the fourth the number of threes. What other year has that property?

While you think about that here are some of the key resources added to the Transum website during the last month.

Particular Pipes is an exercise in adding decimals, fractions or percentages. A number of 'pipe parts' are provided and you have to decide what combination of these parts will make the given length exactly. This is a drag and drop exercise.

New Maths Learning Resource

 

Square and Cube Roots was created following a suggestion from a keen Transum user. It is an exercise in first finding the prime factorisation of a number and from that deducing the square or cube root.

New Maths Learning Resource

 

I would think that right now you are starting to think about a new Term or even a new School Year (if you are in the southern hemisphere). Don’t forget that there is a Back To School collection of activities available to you on the Transum website. Relevant to this time of year I’d like to mention that the Dodecahedral Calendar for 2020 is waiting for subscribers to print out and construct producing a useful item of desk furniture for the coming year.

Back To School

 

The Brackets online exercise is the latest activity to have a set of help videos made for it. While doing the exercise pupils can click on the help tab to see a reminder of how to answer the questions.

Expanding Brackets

 

I am horrified to report that there was a mistake in last month's puzzle. I typed in 18 instead of 10 but have now corrected the error and the correct version can now be found here.

The answer to this month’s puzzle is -1010.

My method was to consider all the pairs of consecutive numbers up to and including 2020 beginning with {1,2}; there are 1010 of them.

Subtracting the odd number from the even number in each pair gives a difference of one and there are 1010 of them. One multiplied by 1010 is 1010.

However the puzzle stated that we should only consider numbers less than 2020 so there are only 1009 pairs with the odd number 2019 left over at the end.

Hence the result is 1009 – 2019 = -1010

The other year with the digits-describing-number-of-digits property is 1210.

That's all for now,

John

P.S. Why is a dog with a bad foot like adding 6 and 7?

A. Because he puts down three and carries the one.


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