When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101. 50 X 101=5,050.Now find the sum of all the digits in integers from 1 through 1,000,000,000.That's all the digits in all the numbers, not all the numbers themselves. -Riddles

When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101. 50 X 101=5,050.Now find the sum of all the digits in integers from 1 through 1,000,000,000.That's all the digits in all the numbers, not all the numbers themselves. -Riddles
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1 Answer

Answer :

The numbers can be grouped by pairs: 999,999,999 and 0; 999,999,998 and 1' 999,999,997 and 2; and so on.... There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then: (500,000,000 X 81) + 1= 40,500,000,001.
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Related questions

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I am a five-digit whole number, read the same forward, backward and upside down. My second digit is half my third digit; my fifth digit is the product of my first and last digits; and the sum of my whole is ten. What am I? -Riddles

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A magician was boasting one day at how long he could hold his breath under water. His record was 6 minutes. A kid that was listening said, 'that's nothing, I can stay under water for 10 minutes using no types of equipment or air pockets!' The magician told the kid if he could do that, he'd give him $10,000. The kid did it and won the money.Can you figure out how? -Riddles

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Last Answer : The kid filled a glass of water and held it over his head for 10 minutes.

A magician was boasting one day at how long he could hold his breath under water. His record was 6 minutes. A kid that was listening said, 'that's nothing, I can stay under water for 10 minutes using no types of equipment or air pockets!' The magician told the kid if he could do that, he'd give him $10,000. The kid did it and won the money. Can you figure out how? -Riddles

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Last Answer : The kid filled a glass of water and held it over his head for 10 minutes.

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Last Answer : 2 - 5 - 8 - 11 - 14 - 17 - 20 - 23 - 26

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Description : Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB( ... ,18)} (D) {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}

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In the same way you can make four fives in an equation to equal 100, (5+5)X(5+5)=100, can you make an equation with only four sevens and no other digits to make 100? -Riddles

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Last Answer : (7/.7)X(7/.7)=100 As 7/.7 = 10 The equation becames equivalent to 10X10

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A 3-input neuron is trained to output a zero when the input is 110 and a one when the input is 111. After generalization, the output will be zero when and only when the input is? a) 000 or 110 or 011 or 101 b) 010 or 100 or 110 or 101 c) 000 or 010 or 110 or 100

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