At the outset, we observe that:
561728395^2 - 438271606^2
= (561728395 - 438271606)*(561728395 +438271606)
= (1,000,000,001)*(123456789)
=123456789123456789
Then, we must have:
561728395^2
= (561728395^2 - 438271606^2)+438271606^2
= 123456789123456789 (calculated) + 192082000625819236 (given)
= 3155387897492760625
Now, manually summing the digits (and then verifying it by calculator), we have:
the required sum of the digits as 91.
Edited on March 22, 2022, 2:00 am
Analytical Solution to the Puzzle
