FOR CHILDREN

PROBLEM # 1
Find the least positive integer such that when its leftmost digit is deleted, the resulting integer is 1/29 of the the original integer.

FOR GROWNUPS

PROBLEM # 2
Let N be the number of consecutive 0's at the right end of the decimal representation of the product 1!2!3!4!....99!100!. Find the remainder when N is divided by 1000.

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SOLUTIONS TO PROBLEMS ON 05/18/06

FOR CHILDREN

PROBLEM # 1
A planet has two moons. One moon rotates about the planet in 32 days while the other moon rotates in 44 days. If  both moons are full tonight, how long will it be before they are both full moons again?

SOLUTION
352/3 days.

FOR GROWNUPS

PROBLEM # 2
My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 140  years. Can you tell me my age in years?"

SOLUTION
84 years.

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