Here are three sequences. I have given the first four numbers, give the fifth and sixth number. All of them can be linked to famous mathematicians, try identifying the mathematician. TO GET COMPLETE CREDIT YOU JUST HAVE TO GIVE 5TH AND 6TH NUMBERS OF SEQUENCES BELOW

FOR CHILDREN

PROBLEM # 1

1,2,4,8,...

PROBLEM # 2

1,1,2,3,.....

FOR GROWNUPS
This is a challenging one. ( Hint: linked to a very famous Swiss Mathematician)

PROBLEM # 3
1,5, 61,1385,.....

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SOLUTIONS TO PROBLEMS ON 12/18/03

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.

SOLUTION

30

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)?

SOLUTION

28.57%

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).)

SOLUTION

Provided by Manivannan Muniyandi of MIT

From the starting point the camel has to travel 3 times since there are 3000 bananas. But the cost of traveling each mile is 5 bananas. (2*3 -1 =5 since last time the camel does not have to travel back). With this cost, how long the camel take bananas until there are 2000 bananas.

5d = (3000 - 2000) = 1000; therefore d = 200.

So, when the camel reaches 200 miles, it would trasported all the bananas across and would have spend 1000 bananas. Remanainng bananas are 2000.

At this stage, the cost of moving each banana for a mile is 3. (2*2-1 = 3 since the second time the camel does not have to return). WIth this cost, how many miles could the camel trasport until there are 1000 bananas. Because once there are 1000 bananas, we could direclty take everything in one shot; no need to return.

3d = 1000; d = 333.33

At this stage, the camel has travelled 200+333.33=533.33 miles. At this stage, the camel has 1000 bananas. Remaining miles are 466.66. Each banana for a mile it cost 466.66 bananas. Remaining bananas are 533.33, that the camel would take to the other side.

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