These problems raise even more questions . . .
Are we allowed to use the Greatest Integer Function?Q1) Total number of squares of any size (side being natural nos.)
. . . in an rectangle . . .
. . = the greatest integer less than or equal to
Basically, it is a "round down" function.
Then we count the number of squares of various sizes . . .
. . . . . . . . .
Then add these numbers.
(a) If the 18 children are distinguishable (they have different names),Q2) In how many ways can 15 boys and 3 girls can sit in a row
. . . such that between the girls at most two sit?
. . then their order must be considered.
(b)If the 15 boys and 3 girls are indistinguishable (arrange 15 blue marbles
. . and 3 red marbles in a row), the problem is still quite difficult.