Math Olympiad Strategies

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Presentation transcript:

Math Olympiad Strategies Drawing a Picture or Diagram

The Tournament The eight teams of the City League will determine this season’s champion with a single-elimination tournament. How many tournament games will the championship team have to play?

Answer: The championship team will have to play three tournament games in all.

Rod Measures The length of three rods are 6 cm, 9 cm, and 11 cm. How can you use these rods to measure a length of 14 cm? 6 centimeters 9 centimeters 11 centimeters

9 + 11 – 6 20 – 6 14 centimeters Answer to Rod problem Place rods with 9cm and 11 cm together. Place 6 cm rod on top and subtract. 9 + 11 – 6 20 – 6 14 centimeters

Drawing a Picture or Diagram Homework NAME________________________________ Due:______________________ 1. How many tournament games will the champion have to play if there are 16 teams competing in a single-elimination tournament? 2. How can you use four rods that measure 2 cm, 5 cm, 7 cm, and 9 cm to measure a length of 1 cm? 3. Making cuts across the diameter, a lumberjack can cut a log into 4 pieces in twelve minutes. How long would it take to cut a log of the same size and shape into 6 pieces? 4. Three containers have capacities of 3, 5, and 9 liters. How can you use these containers to measure exactly 7 liters of water? 5. Assuming that each corner must be tacked, what is the least number of tacks that you need to display 4 rectangular pictures of the same size and shape so that they can all be seen? 6. If the number of competitors is odd in any round of a tournament, then one of the competitors is given a “bye” which means that the competitor does not compete in that round. No competitor may have more than one bye in a tournament. What is maximum number of games a champion will have to play if nine competitors are enrolled in a single-elimination tournament?