Holmes was occupying the basket chair and Watson the armchair closer to the fire, musing on how he'd challenge his friend's mental powers. He couldn't think of any brain teasers so he simply chuckled:
"Holmes, could you add up all the numbers from one to a hundred in under a minute?"
Sherlock took the wind out of the good doctor's sails by pausing in his reading, answering, "Let me see, Watson," thinking for ten second seconds, his brain barely moving into gear, before replying:
"5050."
Watson's eyes almost popped out, as he expostulated, "But how? How? How could even you do that in such a short time?"
"Elementary my dear Watson and that's the question I leave you to puzzle over - how did I do it?
Answer
There are fifty pairs of numbers that add to 100 (100+0, 99+1, 98+2, 97+3, etc.) with the number 50 as an unpaired leftover.
He knew 100 and 0 = 100 and 99 + 1 = 100 so he simply miltiplied 100 x50 and added 50, the number in the middle.
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Check for yourself - highlight under the word Answer, Mad Piper.
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