This is about Project Euler #13. You are given a 100 50-digit numbers and are asked to calculate the 10 most significant digits of the sum of the numbers.
The solution threads stated that we are only required to sum, the 11 most significant digits of each number to obtain the answer. Why is this?
Heres a counterexample to that with fewer digits.
Consider a small example, 2 numbers, and we have to find the 4 most significant digits of the sum.
If we consider only the 5 most significant digits, we get 12344+23455 = 35799 => first 4 = 3579
But if we take all 6, we get 123446+234556 = 358002 => first 4 = 3580
So why would summing only the 11 most significant digits of each number yield the correct answer?
(I have tagged this with modular arithmetic as I suspect its related to that, feel free to correct the tags if not)