Math Mania 2015
- At a bake sale, cookies sell for $1.25 each and brownies sell for $1.50 each. If 120 items were sold for a total of $170, how many brownies were sold?
- What is the angle between the hands of a clock at 3:45?
- A square and a regular pentagon are joined along an edge as shown in the figure. A
third regular polygon can be placed at vertex A so that it shares a side with each
of the other two polygons. How many sides does the third polygon have?
- If a fair coin is tossed six times, what is the probability that heads appear exactly three times?
- If x + 1 is a factor of x3 + 3x2 + kx + 6,what must k be?
- A regular octagon (shaded) is inscribed in a square as shown. What is the ratio of
the length of a side of the square to the length of a side of the octagon?
- What’s the radius of the circle passing through the points (0,0), (6,0), and (4,2)?
- Find all real solutions to the equation |log2|log2 x|| = 1.
TIEBREAKER: If one considers patterns that differ by a rotation or by a reflection to be equivalent, there are six essentially different ways of coloring a 2×2 array of unit squares with two colors: