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Can you add them all up?
teacher, quiz, gauss, carl friedrich gauss, carl gauss
30th of May 2004
Many many years ago our math teacher at school left us with a little quiz to think over until the next class. We mustn't use a calculator and back then MS Excel didn't even exist. He told the quiz as a story about the famous German mathematician Carl Friedrich Gauss.
When Carl went to school their math teacher gave the students a numerical task to solve and he who could calculate the answer the quickest would receive an apple as a price. The task was to sum up all the numbers from 1 to 100. So you start with 1, then 2 and the sum is so far 3. Next you add 3 so the sum is now 6 and so on. All the pupils started calculating really hard but Carl raised his hand and answer the correct sum without even writing anything down. The teacher of course asked if Carl had cheated or otherwise how he did it.
So what is the sum and how did Carl managed to calculate it so quickly? You won't need any formulas or any other advanced mathematics to work it out. If you want to use a computer, feel free but do you really have to?
Comment
************** (8:16:09 PM): so its just 101 X 50
************** (8:16:31 PM): because 100 + 1 is 101
************** (8:16:39 PM): 99 + 2 is 101
~~~~~~~~ (8:17:21 PM): so what if its 1-1000
************** (8:17:52 PM): 1001 X 500
where does the 50 come from - i don't get this...
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First realize that:
1+99 = 100
2+98 = 100
3+97 = 100
...
If you keep adding this way excluding the number 50, you will get 4900. Next, add 100 and 50 to 4900. The final answer is 5050.