Math Challenge Problem #14

A Martian College Algebra Textbook was recovered recently from a crashed spaceship. In it was written that the equation has solutions and . This doesn’t look right. However, assuming the Martian Algebra is correct, how many fingers do Martians have? What would the Martians say the solutions to are?

Make sure to give a description of how you found your answers.

Due Monday May 5, 2008

Math Challenge Problem #13

Here are two classic chess board problems. First, how many squares are on an 8 by 8 chess board? Keep in mind that squares larger than 1 by 1 count too. Second, how many rectangles can you find? There are a lot of nice number patterns hidden in the solutions.

Make sure to give a description of how you found your answers.

Due Monday April 28, 2008

Solutions By

Smit Patel

Math Challenge Problem #12

Suppose Alice and Bill are flipping coins. Suppose they take turns and Alice goes first. What is the probability that after three rounds, Bill has had the same result as Alice each time? What is the probability that, after four rounds, they have exactly four heads between them? Finally, what is the probability that Bill is the first one to have a coin land on “heads”? (It is possible, though unlikely, that this could take hundreds of rounds….)

Make sure to give a description of how you found your answers.

Math Challenge Problem #11

Four circles are drawn inside a circle with radius equal to one. The larger two have radii equal to one half. Assuming all of the circles are as large as possible without overlapping, find the radii of the smaller two circles. Also find the coordinates of the centers of the circles if the big circle is centered at the origin.

Make sure to give a description of how you found your answer.

Due Monday April 14, 2008

Math Challenge Problem #10

How many circular disks of diameter 1 inch can you fit (without overlapping) inside an 8 by 8 square?  What percentage of the square is actually covered by the disks? What is the smallest value for “n” for which you can fit more than n2 disks of diameter 1 inside an n x n square? Can you find a formula to give the number of such disks that can fit in an  n x n square?
Make sure to give a description of how you found your answer.

Math Challenge Problem #9

My friend Bob sometimes gets confused; 80% of the time he identifies a sheep as
a sheep, and 80% of the time he correctly calls a goat a goat. (Otherwise, he thinks it's the other animal.)  In his area, 85% of the animals are sheep and the rest are goats.
Bob sees a random animal and says it's a goat. What's the probability that he's right?

Make sure to give a description of how you found your answer.

Due Monday March 31, 2008

Solutions By

Smit Patel

Seth Franke

Math Challenge Problem #8

Suppose you have nine square tiles the sides of which have lengths: 1, 4, 7, 8, 9, 10, 14, 15, and 18 feet.  How can you fit them together into a rectangle? (With no cutting or overlapping, of course.)  To answer, give the coordinates of the lower left corner of each square, starting with the square at (0,0).

Make sure to give a description of how you found your answer.

Due Monday March 3, 2008

Math Challenge Problem #7

If n is a natural number, the reciprocal of n, 1/n, is called a 'unit fraction.'
Historically, numbers were expressed as sums of unit fractions,
 like 4/7 = 1/2 + 1/14 or 1 = 1/2 + 1/3 + 1/6.
Write each of these fractions as sums of distinct unit fractions. Try to use as few unit fractions as possible and to make the sum of the denominators as small as possible.
a) 3/23 . . . b) 14/15 . . . c) 7/11 . . . d) 11/7

Make sure to give a description of how you found your answers.

Due Monday February 25,2008

Math Challenge Problem #6

Find a polynomial equation in terms of x, that has integer coefficients such that  is a solution.  Now find a second polynomial equation in x, with integer coefficients, having   as a solution.

Make sure to give an explanation of how you got your answers.

Math Challenge Problem #5

This week’s problem is really four separate problems. First, show that  is a multiple of 6. Then show that  is a multiple of 3. Now, show that  is a multiple of 13. Finally, show that  is a composite number.

Make sure to give an explanation of how you got your answers. Don’t just use a calculator!

Due Monday February 11, 2008

Math Challenge Problem #4

Suppose you have a box with 15 red marbles and 10 blue marbles. You randomly draw one from the box. You replace it with a new marble of the other color. Then you shake the box and draw a marble at random a second time. What is the probability that the second marble that you draw is red?

Make sure to give an explanation of how you got your answer.

Math Challenge Problem #3

Duels in the town of Peaceful are rarely fatal. By both law and
custom, all duels take place at one location between 5:00 am and
6:00 am. Each dueller arrives at a randomly chosen time, stays for
exactly 5 minutes and leaves. Unless both duellers are there at the
same time, there is no duel. What is the probability that two
duellers will meet?

Make sure to give an explanation of how you got your answer.

Due Monday January 28, 2008

Math Challenge Problem #2

At the beginning of a peace conference between two rival factions, each person shook hands with every other member of his own faction, a total of 406 handshakes. After the conference each person shook hands with every person in the other faction, a total of 414 handshakes. How many people from each faction attended the conference?

Make sure to give an explanation of how you got your answer.

Due Monday January 18, 2008

Math Challenge Problem #1

Find a six digit integer such that if you take the left-most digit and move it all the way to the right, the result is three times the number you started with. For example, change 123456 to become 234561 (but this isn't the answer). Explain how you came up with your answer.

Due Monday January 11,2008