1470.41 – A Giant Sum

Find the sum of these four numbers:

123,654,987,864545,454,545,454898,989,545,636252,252,252,252\begin{array}{l}123,654,987,864 \\545,454,545,454 \\898,989,545,636 \\252,252,252,252\end{array}

The numbers may or may not be too big to fit in your calculator, but you can use it anyway. Just figure out how.

Solution

As it's a sum, we can rearrange the numbers in various ways. For example,

123654987864545454545454898989545636252252252252\begin{array}{llll}123& &654& &987& &864 \\545& &454& &545& &454 \\898& &989& &545& &636 \\252& &252& &252& &252\end{array}

where it must be understood that in the first column of this array the numbers are multiplied by 10910^9, the second column by 10610^6, and the third column by 10310^3. Adding the columns (using a calculator!) and combining with the appropriate powers of 1010 you should get the answer

1,820,351,331,206.1,820,351,331,206.

Did you? Now see if you can think of another way to do this, probably a better one.