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 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?

-------------------------------------------------------------------------------------------------------------

Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-061704 as the subject line. Please include your full name in the text of the main message. The first one to submit the right answer will be profiled in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

-------------------------------------------------------------------------------------------------------------

SOLUTIONS TO PROBLEMS ON 06/03/04

FOR CHILDREN

PROBLEM # 1

A grocer stacks oranges in a pyramid-like 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(x-1) = Mod(x-2)?

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.

|