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Old 2006-10-19, 16:22   #3
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

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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