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.