PROBLEM # 1

A person was born on July 4, 30 B.C. and died on July 4, 30 A.D. How many years did the person live?

FOR GROWNUPS

PROBLEM # 2
Determine the sum of all positive six-digit numbers. Please provide the exact value!

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SOLUTIONS TO PROBLEMS ON 06/17/04

FOR CHILDREN

PROBLEM # 1

12 members were present at a board meeting. Each member shook hands with all of the other members before & after the meeting. How many hand shakes were there?

SOLUTION
132.

FOR GROWNUPS

PROBLEM # 2

A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

x=2233445566,
y=7788990011,
z=9988776655

He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

x^N + y^N = z^N

and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.
How did the boy figure out that the scientist was wrong?

SOLUTION
x^N always ends in 6, y^N always ends in 1 and z^N always ends in 5. If x^N and y^N are added, the result will always end in 7.

Congratulations Rahul Banerjee, Ramesh Gupta, Vipul Joshi, Swathi Krishnan, Samita Mohanasundaram, Mukund Seshadri and Bharath Venkataraman who were winners of the last set of puzzles.

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