Briefly

Add all 4-digit numbers

Add all 4-digit numbers

Without the help of the calculator and in a reasonable time, take all 4-digit numbers, that is, from 1000 to 9999 and add them.

What's the score?

Solution

One possible way to do this could be the following:

We calculate the sum of the numbers from 1 to 9,999 and then subtract the sum of the numbers from 1 to 999 since they should not have been taken into account. This is done to facilitate the calculations:

To add all the numbers from 1 to 9999 we look at that:

1 + 9999 = 10.000
2 + 9998 = 10.000
3 + 9997 = 10.000

and so on until:

4.999 + 5.001 = 10.000

Total = 4,999 times 10,000 plus the number 5,000 that we have not included = 49,995,000

But here we have added the numbers from 1 to 999 that should not be taken into account since they do not have 4 figures. Thus, with the same system we calculate the sum of all the numbers from 1 to 999 and then subtract it from the total previously calculated:

1 + 999 = 1.000
2 + 998 = 1.000
3 + 997 = 1.000

and so on until:

499 + 501 = 1.000

Total 499 times 1,000 plus the number 500 that has no "partner" = 499,500

If we subtract it from the previous result we have 49,995,000 - 499,500 = 49.495.500