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# An alternating squares "aha" puzzle

8 replies to this topic

### #1 bonanova

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Posted 12 October 2013 - 09:42 AM

Evaluate 1002 - 992 + 982 - 972 + 962 - 952 + ... + 22 - 12 = ?
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### #2 kukupai

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Posted 12 October 2013 - 03:50 PM

Spoiler for could it be

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### #3 joehx

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Posted 12 October 2013 - 07:33 PM

Spoiler for Spoiler

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### #4 bonanova

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Posted 12 October 2013 - 07:48 PM

Spoiler for Spoiler

Hi Joe, and welcome to the Den.

Pairing is the right first step. Can you make the pairs even simpler?
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### #5 kukupai

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Posted 12 October 2013 - 08:23 PM   Best Answer

Spoiler for

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### #6 joehx

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Posted 12 October 2013 - 08:24 PM

I'm not sure it makes it any easier but you could pair from opposite ends, like in the sum to n.

Spoiler for Doing this

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### #7 bonanova

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Posted 12 October 2013 - 08:38 PM

Good job all. Several great answers.

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### #8 witzar

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Posted 14 October 2013 - 01:39 PM

Spoiler for (almost) no calculations at all

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### #9 bonanova

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Posted 15 October 2013 - 06:42 PM

Spoiler for (almost) no calculations at all

Nice.
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