Answering a question by asking Questions...

• Do you have only 400 of each book? or Do you want to send each school 400 books in each box??? you are not clear.
• How many books does each school need (as many as you can give them??)

if 1st choice (400 of each book):

I propose for each book ($qty=400?)

1. Get number of schools needing it $n
2. min books per school $bps= int($qty/$n);
3. get extra books $extra=$qty-$bps*$n;
4. give 1 extra book to schools (start alphabetically)

if 2nd choice (400 books/box, many boxes/school):

I think yu could probably use statistics... evaluate the needs of each school.... do you need an exact solution? do you have time to bruteforce it?