301 eggs
When dividing the eggs by 2-6 one egg is left. The smallest  number that can be divided by 2,3,4,5,6 is 60. So we start with 61 and continue with steps of 60 until we find the number.

4 years. The trees grow one inch every year and the river rises 2 inches every year, hence every year the gap of 4 inches decreases by one inch. So after 4 years the level of the water will be exactly at the base of his house

Answer: 16 or 20
Explanation:
In case on each  line are 5 children then if we start from top and go clockwise that we have number 6 is the 2nd on the right  line (5-9) and 16 will be the 2nd on the left line (13-1>> 13,14,15,16,1). so 16 in total
In case on each line are 6 children then if we start from top and go clockwise that we have number 6 on the top right corner (1-6) and 16 will be on the bottom left corner (11-16) they are standing in opposite sides of the diagonal line that can be drawn between the top right corner and the bottom left corner, so 20 in total.

Four

The puzzle is not clear.

it was daylight

Answer: 24 zeroes.

Explanation:
When yo want to know how many times the digit 0 appears at the end of the number X, you have to remember that the answer is exactly the number of times that X is divisible by 10.
The meaning of ” X is divisible by 10″ is that X is divisible by 2 and 5 together. In the list of numbers from 1 to 100, every even number is divisible by 2 and only every fifth number is divisible by 5. Therefore, the number
of times X is divisible by 5 is less than the number of times X is divisible by 2. Therefore the number of times X is divisible by 5 is what determines the number of times it is divisible by 10. Hence, if we find how many times 5 participates in the product that creates 100!, we will get the solution.

Let’s look at the multiplication of the numbers from 1 to 100 and start replacing the number 5 with 5*1, the number 10 with 5*2  and so on.  Thus we will get 20 occurrences of 5.  But we must notice that in the four numbers 25, 50, 75, 100 the number 5 participates not once but twice (25 = 5*5, 50 = 5*5*2, 75 = 5*5*3, 100 =  5*5*4) so we have 4 more fives so in total we have 5 participating 24 times.

If a normal cup is 200ml than after 9 friends there will be less than 1ml and it is not reasonable that a person will want to drink such amount. So practically 9 cups

The doors that are left open are a the numbers that have a perfect square root : 4,9,16,25,36,49,64,81,100

Because they have odd number of dividers, and that means that the last monkey that can get to the door will open it.