MATHCOUNTS is a national mathematics competition and organization supported by the National Society of Professional Engineers. Beginning in 1982, it sponsors local, state, and national competitions to promote mathematics achievement at the middle school level. As a MATHCOUNTS coach at a local middle school and avid geocacher, I have set up geocache events for the kids I coach and for local middle school math camps, where kids have to solve MATHCOUNTS problems which allow them to determine the coordinates of a geocache. This cache is the 5th in a series of math geocaches dedicated to one of the kids I have coached, and part 2 of a 5-part cache series at the university. Please note the clue written on the log sheet for this cache. You will need to collect the clues from each of MC – Julia, MC – Tarl, MC – Magnolia, and MC – Stellan to find the 5th and final cache of this university series: MC – Bente.
The cache is NOT AT THE POSTED COORDINATES. The coordinates given will take you to the Oval at The University of Montana from where you will have a short walk to the cache. To find this cache, you will need to solve the following two MATHCOUNTS problems and use your answers to determine the coordinates. The answer to the 1st question is a 2-digit integer AB and the answer to the 2nd question is a 2-digit integer CD divided by a 2-digit integer EF. When you solve these questions, you will plug your answers into the coordinates: N 460 51.(E-B)(A+B)D, W 1130 58.(A+C-F)(B+C)E to determine the cache location.
MATHCOUNTS Problems:
1. Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it will take 1.5 hours, and with only valves B and C open it takes 2 hours. How many minutes will it take to fill the tank with only valves A and B open? Answer: AB
2. A forest contains 15 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 15 elk are captured. Assuming that elk are captured independently of one another and that each elk has the same chance of being captured, what is the probability that exactly 2 of these 4 elk have been tagged? Express your answer as a common fraction. Answer: CD/EF
The cache container is a small magnetic key holder, and contains only a log. Since this cache is hidden at the university, you will need to use extreme stealth at certain times of the day. Be patient and if possible, try to look for this cache while most students are in classes.
The level of difficulty for this cache refers to both the puzzle and the cache.
You can check your answers for this puzzle on GeoChecker.com.