The 100 Days of Christmas

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The 100 Days of Christmas

Post  Archis on Thu Dec 25, 2008 7:30 pm

In the 100 days of Christmas, on the last day of Christmas the beneficiary receives 100 ducks a quacking, 99 golden bonnets, 98 roasted pheasants and so on until 1 partridge in a pear tree.

How many presents did he receive in total on that last day?

HINT:
Spoiler:
It's basically the sum of arithmetic series with a common difference of 1 and initial term of 1. So it's just the sum of an arithmetic series.

#of terms * (first term+last term)/2
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Re: The 100 Days of Christmas

Post  Angelica K on Tue Feb 10, 2009 3:15 am

Is it...

Spoiler:
5050
My logic: Imagine we're dealing with 1,2,3,4,5,6. That can be split into 1+6, 2+5, and 4+3, or 7 times 3. In other words, N+1 times N/2. In this case, 101 times 50. That's quite a few presents!

And your creative future presents rock.
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Re: The 100 Days of Christmas

Post  Archis on Thu Feb 12, 2009 4:06 am

Correct. The answer is 5050.

Clever reasoning and well done. For those interested in similar strategies, a Google search of Karl Gauss may be beneficial. (He is the most known to use this strategy)

It can be further added that when you are adding any series 1+2+...+n, the answer is n(n+1)/2. Likewise here it would be noted as 100(101)/2
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