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 are too big to fit in your calculator, but you cancan 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.