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PostPosted: Thu Jan 13, 2022 11:45 am 
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Joined: Wed Sep 18, 2019 2:57 pm
Posts: 43
Hi,
I see the following question in a “Non-Routine Maths problems” for 11+

Find the sum of the integers from 1 to 1000.

1+2+3+4…………………………………………….+998+999+1000=?


I know the answer is simply n(n-1)/2 i.e 1000*999/2 … and that because I have a degree in applied Maths. My question is…. how is this an 11 plus question? How is a 10 year old suppose to think of this without have to used some advance maths summation result?
Funny enough my daughter came across the solution herself whilst reading “Women in Science” – 50 Fearless Pioneers who changed the world. I was pretty impressed she recognised that was the solution right in the middle of Maryam Mirzakhani's brief biography.


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PostPosted: Thu Jan 13, 2022 7:44 pm 
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Joined: Wed May 09, 2007 3:09 pm
Posts: 1280
Location: Solihull, West Midlands
Isn't this the one some young genius (Leibnitz? Pascal? Fermat?) is supposed to have solved in an instant when his teacher set it to keep the class occupied for an hour?

I would agree that in an 11+ it would only be likely to be solved either by someone similarly with a quick brain who spots that they can add two copies of the numbers together in matching pairs 1+1000, 2+999 ..... 1000+1 , realise that they have 1000 * 1001 and halve it - or who has read widely in enrichment maths and been shown it before. Maybe it's the scholarship question.....


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PostPosted: Mon Jan 31, 2022 12:51 pm 
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Joined: Wed Sep 18, 2019 2:57 pm
Posts: 43
Hi,
Just thought i would drop an update here.....and a answer to my own question.
First a correction to the above, the solution is n(n+1)/2 and NOT n(n-1)/2.


This question is actually related to Triangular numbers. Precisely, the sum of first n numbers is the nth triangular number.
so essentially in the question above, we are to calculate the 1000th Triangular number. Notice that the formular for the nth triangular number and the sum of the first n numbers are the same. The visual below may be helpful.

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PostPosted: Wed Feb 02, 2022 4:50 pm 
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Joined: Wed Mar 04, 2009 3:01 pm
Posts: 10748
Location: Herts
Sometimes the maths questions at the end of the paper are put there to keep the students occupied who have almost finished the paper and who might otherwise become restless and distract the other students.

Dd1 had this question as the last one in a Maths paper a few years ago. DG


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