Hello, Navesh!

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 theirordermust 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.