I was interested to hear recently a little tale about German mathematician, astronomer, and physicist Johann Carl Friedrich Gauss (1777 - 1855).

When he was at junior school the teacher (obviously requiring an hour or two's respite) asked the class to sit and add up all the numbers from 1 to 100. 1 +2 +3 + 4 etc.

He was mortified to glance up and see young Gauss with his hand aloft 25 seconds later to declare that he'd finished and the answer was 5,050.

Gauss's mathematical brain had spotted a pattern in the task that meant the answer could be determined by a single multiplication rather than 100 additions.

I'd be interested to know if anyone can spot the short-cut without referring to Mr Google. The answer will be shown in the first comment so it's not a competition.

So just settle down with your excercise books and keep quiet at the back there.....

## 9 comments:

OK class, here's the answer.

Imagine all the numbers from 1 to 100 and keep taking the first and last together as pairs and add them. You'll end up with:

100+1, 99+2, 98+3 etc down to 51+50.

This gives you 50 pairs, all with the same total of 101.

50x101 = 5050.

Simples!

Very clever. I wouldn't have got that in a million years. My brain just doesn't work that way :(

PS. HAHAHA - just noticed my "anti-spam word" is... brain. Something we've established, I don't have!

Well, dang! I was going to put the solution on line for a modest sum but you've cunningly forestalled me. I may have to consider suing for loss of earnings.

I thought it was 505 x 10.

Well beyond my capabilities, I shall put it to the two eldest offspring, they are A Level maths bods!

So efficient these Germans...

Dagnabbit! I didn't even understand the answer!!

Nutty: I thought your word was "Brian".

Christopher: Google must be a nightmare for teachers these days!

Dave: Lateral thinking as always.

Jon: I was doing some "bytesize" GCSE Maths on my iPhone this morning before I got up. I must get out more...

Macy: I believe it was a German Spice Biologist who made the trains run on Thyme.

Lesley: Like all creative arists you have a good excuse!

They must have taught us well in Kent because I can remember this from O level maths, and I only got a C. Apparently nowadays if you can actually manage to spell your name correctly and remember your house number by the time you're 15, you don't need to turn up for the exam.

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