FOR CHILDREN

PROBLEM # 1

In a rectangle, the ratio of the diagonal to the perimeter is 5 to 14 while the area is 432. Calculate the length of the diagonal.

PROBLEM # 2

If you got a 40% discount on a $150.00 pair of sport shoes and 20% of a $200 set of roller blades, what was the percent discount on the total purchase (assuming no taxes are involved)?

FOR GROWNUPS

PROBLEM # 3
Submitted by Kanchi Gandhi

Camel Crossing the Desert Problem

A camel is sitting by a stack of 3,000 bananas at the edge of a 1,000-mile-wide desert. He is going to travel across the desert, carrying as many bananas as he can to the other side. He can carry up to 1,000 bananas at any given time, but he eats one banana every mile. What is the maximum number of bananas the camel can get across the desert? How does the camel do it? (Hint: The camel can take several trips, but eats a banana for each mile (forward or backward).)

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SOLUTIONS TO PROBLEMS ON 12/04/03

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?

SOLUTION

55.

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?

SOLUTION

4 came to the party and 8 ate chips (at home or at the party).

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?

SOLUTION

It is the only solution I could determine.

WINNERS

Congratulations to Devika Ranjan, who were all winners of the last puzzle.

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