In just a few weeks, 224 Mathletes® will arrive in Boston, MA to take part in the 2015 Raytheon MATHCOUNTS National Competition. These are some of the best middle school math students in the country. See if you can solve a few of the problems that made them 2015 state champions!
Iniki has large, medium and small metal bars. The large bars each weigh 8 kg. The medium bars each weigh 6 kg. The small bars each weigh 3 kg. Iron, nickel and lead are present in the ratio 4:1:3 in each large bar, 2:1:3 in each medium bar and 1:1:1 in each small bar. If Iniki wants to melt together a combination of bars to make an alloy that contains 40 kg of iron, 20 kg of nickel and 40 kg of lead, how many small bars will she have to use??
A building constructed in January of the year 2000 will celebrate its 1-month anniversary in February of 2000 and its 12-month anniversary in January of 2001. If during the year n this building will celebrate its n month anniversary, what is the value of n?
Using the figure of 15 circles shown, how many sets of three distinct circles A, B and C are there such that circle A encloses circle B, and circle B encloses circle C?