For The Mathematically Inclined


Anil Saigal 06/06/2004
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?
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 10years 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?

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 SOLUTIONS TO PROBLEMS ON 06/03/04
FOR CHILDREN
PROBLEM # 1
A grocer stacks oranges in a pyramidlike stack whose rectangular base is 5 oranges by 8 oranges, Each orange above the first level rests in a pocket formed by four oranges in the level below. The stack is completed by a single row of oranges. How many oranges are in the stack?
SOLUTION
100.
PROBLEM # 2
What is the value of x if:
Mod(x1) = Mod(x2)?
SOLUTION
1.5.
FOR GROWNUPS
PROBLEM # 3
What is the next number in the sequence:
1, 9, 18, 25, 27, 21,....
Explain your answer.
SOLUTION
4. Congratulations Mukund Seshadri and Sanjay Yengul who were winners of the last set of puzzles.

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