#### 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. Answer: 50 X 101=5,050. What is 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.)

**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.

**Solution: **

## Show 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.

## Show 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.

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.

#### Share with

Facebook Comment

#### You may also like..

#### How is it possible to always find what your looking for in the last place you look?

**Answer: ** If you find what your are looking for then you would stop looking so it would be in the last place you look.

**Solution: **

#### How can you tell an ant’s gender?

**Answer: **Put it in water. If it sinks it’s a girl ant, If it floats it’s buoyant

**Solution: **

#### When one does not know what it is, then it is something; but when one knows what it is, then it is nothing. Riddle answer

**Answer: **Riddle

**Solution: **

**#Riddle_answer: **

## When one does not know what is that, then it is something; but when one knows what it is, then it is nothing. what is that? Riddle answer …

##### Show answer

**Correct answer : Riddle**

Cheers !!!

#### Also read : How many chickens and cows puzzle answer

**Knowledge increases by sharing 🙂**

**#Riddle_answer: **

## When one does not know what is that, then it is something; but when one knows what it is, then it is nothing. what is that? Riddle answer …

##### Show answer

**Correct answer : Riddle**

Cheers !!!

#### Also read : How many chickens and cows puzzle answer

**Knowledge increases by sharing 🙂**

**Previous**

**Next**