Problem #29

A regular hexagonal pyramid has one of its lateral edges four times the length of one side of the base.  If the volume of the pyramid is 60 cubic centimeters, compute the number of centimeters in the length of one side of the base in simplest radical form.

Problem #28

Compute the number of perfect square factors in the base ten number , where n! represents n factorial.

Problem #27

In the game Combat, a red army is worth 10 points, a blue army is worth 3 points, and a white army is worth 1 point.  While I am playing I notice that the value of my red armies is worth 40 points more than the total value of my blue and white armies.  Also, the number of red armies is one-third the total number of blue and white armies and all of my armies are worth a total of 240 points.  How many total armies do I have?

Problem #26

The sides of a triangle are of length 4,   and x.  Determine all of the possible integer values of x such that the largest angle of the triangle is less than 90 degrees.

Problem #25

Given the set of natural numbers, {1, 2, 3, 4,…}, find the 2010^th number in this set that is not divisible by 2 or 3.

Problem #24

Russell has $7.85 in nickels, dimes and quarters.  He has nine more quarters than nickels.  If Russell has at least one of each type of coin, what is the difference between the most number of coins and the least number of coins that Russell can have?

Problem #23

Let A(2, 0), B(3, 5) and C(0, c).  Find all of the values of c that make triangle ABC a right triangle with the right angle at point C.

Problem #22

Urn A contains 8 balls, each are either red or yellow.  Also, urn B contains 3 red balls and 2 yellow balls.  Each day, at noon, a ball is randomly drawn from urn A and placed into urn B.  Every midnight a ball is randomly chosen from urn B and its color is noted.  Then, all of the balls are returned to their original urn for the next day’s drawing.  The midnight ball is yellow 3/8 of the time.  How many yellow balls are in urn A?

Problem #21

One day, Charlie drove to work at an average speed of 40 miles per hour and arrived one minute late.  The next day, Charlie drove to work at an average speed of 45 miles per hour and arrived one minute early.  If he drove the same route each day, how far does Charlie drive to work (in miles)?

Problem #20

Consider a cube with edge length 4.  If the centers of the adjacent faces of the cube are joined in pairs, then an octahedron is formed.  Find the total surface area of this octahedron.  Please express your answer in simplest radical form.