For The Mathematically Inclined


11/24/2003
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? 
Please send your solutions to anil@lokvani.com.
Use "Problem Solutions M120403" 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 give for
solutions not sent to anil@lokvani.com.
If you need clarification on any problem, please contact anil@lokvani.com.
 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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