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Math Olympiad #80

Math Olympiad #80. 3 minutes. Question 1.

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Math Olympiad #80

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  1. Math Olympiad #80

  2. 3 minutes Question 1 I have a drawer which contains 40 socks in the following numbers and colors: 12 tan, 9 brown, 11 gray, and 8 blue. Suppose I am blindfolded. What is the fewest number of socks I must pick from the drawer to be absolutely certain that I have two socks of the same color among those I have picked? Answer: 5 socks

  3. 5 minutes Question 2 In the equation below, A and B represent counting numbers. What values of A and B will make the equation true? (List the value of A first, and then the value of B.) Answer: A=2 and B=1

  4. 6 minutes Question 3 Using the letters A and B, the following two-letter code words can be formed: AA, AB, BB, BA. Using the letters A, B, and C, how many different three-letter code words can be formed? Answer: 27 code words

  5. 5 minutes Question 4 Below, different letters represent different digits, ABC and DEF are three-digit numbers, and neither of the lead digits A and D is zero. If DEF is subtracted from ABC, what is the largest remainder that can occur? A B C - D E F Answer: 885

  6. 6 minutes Question 5 Triangle ABC has its vertices A, B, and C on the sides of a rectangle 4 units by 5 units as shown. What is the area of triangle ABC in square units?

  7. 6 minutes Question 5 Triangle ABC has its vertices A, B, and C on the sides of a rectangle 4 units by 5 units as shown. What is the area of triangle ABC in square units? Answer: Area of Triangle ABC is 9 square units

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