Level 12: The other guy is unusually herding ducks Forced to get the new row out. Row 2 is not enough. Row 3 has one left over. Row 4 is still not complete. Row 5 is missing a new duck. Line 7. How beautiful is the Duck? Calculate the new talent. (I know the number of ducks is less than 200).

Let the number of ducks be x (x∈N^*).

Since row 5 is missing 1 child, x divided by 5 leaves a remainder of 4 ⇒ x has a digit ending in 4 or 9.

Since rows 2 and 4 are not stackable, x is not divisible by both 2 and 4 .

⇒ x has a digit ending in 9.

Since the number of ducks can be arranged in 7 rows, x⋮7.

Hence x ∈ B(7), x ends with 9 and x < 200, so x ∈ {49; 119; 189}.

And x divided by 3 leaves a remainder of 1, so x = 49.