Mathematics Genie

Puzzle for the week..
QUESTION: An apple vendor has 1000 apples and 10 empty boxes. He asks his son to place all the 1000 apples in all the 10 boxes in such a manner that if he asks for any number of apples from 1 to 1000, his son should be able to pick them in terms of boxes.
How did the son place all the apples among the 10 boxes, given that any number of apples can be put in one box.

ANSWER: 1, 2, 4, 8, 16, 32, 64, 128, 256, 489

Puzzle for the week..
QUESTION: An apple vendor has 1000 apples and 10 empty boxes. He asks his son to place all the 1000 apples in all the 10 boxes in such a manner that if he asks for any number of apples from 1 to 1000, his son should be able to pick them in terms of boxes.
How did the son place all the apples among the 10 boxes, given that any number of apples can be put in one box.

Puzzle for the week..
QUESTION: Four friends decided to go on a vacation to a hill station. During their vacation, they experienced 13 days of heavy snowfall. When it used to snow in the morning, the afternoon was clear, and when it used to snow in the afternoon, the day was followed by a clear morning.
In total, they had eleven clear mornings and twelve clear afternoons. Is there a way you can calculate the number of days they spent in their vacation?

ANSWER: 18

Explanation:
Number of days with snow in morning and clear afternoon = A
Number of days with clear morning and snow in afternoon = B
Number of days with no snowfall in morning or afternoon = C

Now, number of days with snowfall = A + B = 13
Number of days with clear mornings = B + C = 11
Number of days with clear afternoons = A + C = 12
Adding these three equations, we get
2 * (A + B + C) = 36
Or, A + B + C = 18

Puzzle for the week..
QUESTION: Four friends decided to go on a vacation to a hill station. During their vacation, they experienced 13 days of heavy snowfall. When it used to snow in the morning, the afternoon was clear, and when it used to snow in the afternoon, the day was followed by a clear morning.
In total, they had eleven clear mornings and twelve clear afternoons. Is there a way you can calculate the number of days they spent in their vacation?

Puzzle for the week..
QUESTION: Each child in a family has at least 2 brothers and 4 sisters. What is the smallest number of children the family might have?
ANSWER: 8

Puzzle for the week..
QUESTION: Each child in a family has at least 2 brothers and 4 sisters. What is the smallest number of children the family might have?

Puzzle for the week..
QUESTION: Mom and Dad have four daughters, and each daughter has one brother. How many people are in the family?
ANSWER: Seven. The four daughters have only one brother, making five children, plus mom and dad.

Puzzle for the week..
QUESTION: Mom and Dad have four daughters, and each daughter has one brother. How many people are in the family?

QUESTION: Six glasses are in a row. The first three are full of juice; the second three are empty. By moving only one glass, can you arrange them so empty and full glasses alternate?
ANSWER: Pour the juice from the second glass into the fifth glass.

Puzzle for the week..
QUESTION: Six glasses are in a row. The first three are full of juice; the second three are empty. By moving only one glass, can you arrange them so empty and full glasses alternate?

Puzzle for the week
QUESTION: I am a three-digit number. My tens digit is five more than my ones digit. My hundreds digit is eight less than my tens digit. What number am I?
ANSWER: 194