Barbie the Computer Engineer, Remixed
themarysue.com4 pointsby phj0 comments
A C E
* B D
To make it more clear what to do next, you can just append a zero onto the number "BD" and still solve the same problem, because instead of multiplying "ACE" * "BD", you are multiplying "ACE" * "BD0" = ("ACE" * "BD") * 10: A C E
* B D 0
Now, to figure out which of the two greatest digits are A and B, and which of the next two greatest are C and D, you can apply the identity (x + y) * (x - y) = x^2 - y^2 to this. Since "ABC" * "BD0" = (x + y) * (x - y), then equating "ABC" = x + y and "BD0" = x - y, you can solve to get x = ("ACE" + "BD0") / 2, which is the same number no matter the order between A and B, or between C and D. Then maximizing (x + y) * (x - y) means minimizing y^2; or, making the two numbers "ACE" and "BD0" as close together as possible, which leads to the given solution.
The meeting offices are mentioned briefly, but those see quite a bit of use as well.