FOR CHILDREN

PROBLEM # 1

There are exactly 11 people in a room and each person shakes hands with every other person in the room. When A shakes with B, B is also shaking with A. That counts as ONE handshake. How many handshakes will there be when everyone is finished?

PROBLEM # 2

Binky invited 12 friends to her Super Bowl Sunday party.
1/3 of them came to the party.
1/2 of them ate wings.
4/6 of them ate chips.
How many came and ate chips?

FOR GROWNUPS

PROBLEM # 3
Submitted by Ritesh Agarwal

Can you solve for [x, y] in this Diophantine equation 25x^2 + 39x + 38 = y(y+1) where x and y are natural numbers. One solution is [3, 19]. The question is can you find out how many solutions exist? If more than one then what are the other solutions and if just one then prove that only one solution exists?

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SOLUTIONS TO PROBLEMS ON 11/20/03

PROBLEM # 1

A little green frog is sitting at the bottom of the stairs. She wants to get to the tenth step, so she leaps up 2 steps and then back 1. Then she leaps another 2 steps and back 1. How many leaps will she have to take, if she follows this same pattern, till she reaches the tenth step?

SOLUTION

9 leaps.

PROBLEM # 2

If you were given the choice between taking 5000 dollars or 1 penny a day doubled each day for 20 days, which one would you choose and why?

SOLUTION

1 penny a day doubled each day for 20 days.

PROBLEM # 3

Two vertical poles 12 ft apart are 6 ft and 12 ft in height. A rope is stretched from top of each pole to the bottom of the other. How far above the ground do the ropes cross?

SOLUTION

4 ft. above the ground.

WINNERS

Congratulations to Jayakrishnan Menon, Raghav Ranjan, Mukund Seshadri and Sumanth Shankar, who were all winners of the last puzzle.

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