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Old 2006-10-19, 14:19   #1
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"Tim Sorbera"
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How do you calculate (and what is) 1+2+3+4...97+98+99+100 in under 10 seconds?
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Old 2006-10-19, 14:39   #2
retina
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Divide into 2 sets, 1-50 & 51-100
Reverse the order of the second set
Imagine the second set written below the first set
Add each vertical pair (the pattern emerges), all pairs add to 101
Clearly there are 50 such pairs
Answer is 101*50


This is the arithmetic progression

Last fiddled with by retina on 2006-10-19 at 14:45 Reason: spoiler tags added
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Old 2006-10-19, 16:22   #3
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"Tim Sorbera"
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Quote:
Originally Posted by retina View Post
Divide into 2 sets, 1-50 & 51-100
Reverse the order of the second set
Imagine the second set written below the first set
Add each vertical pair (the pattern emerges), all pairs add to 101
Clearly there are 50 such pairs
Answer is 101*50
The way I found was the same, except you added 1+99, 2+98...49+51 to get 49 100s (4900) then added the 50 and the 100 that were left over (because neither of them could be added to something different to make 100), to get 5050.
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Old 2006-10-19, 17:14   #4
mfgoode
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Thumbs up Arithmetic progression.


Sorry to correct you but Retina is right, tho' you are also right tho' your method is not orthodox.
This problem was solved in a jiffy by Gauss, when he was 6 yrs. old , one of the three greatest mathematicians, who ever lived,[ Archimedes, Newton and Gauss]
I'm glad you mentioned it as it has refreshed my aging memory.

Mally

Last fiddled with by mfgoode on 2006-10-19 at 17:16 Reason: Add on
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