Download - Math Olympiad #80
Math Olympiad #80
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?
3 minutes
Answer: 5 socks
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.)
5 minutes
12
11
43
BA
Answer: A=2 and B=1
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?
6 minutes
Answer: 27 code words
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
5 minutes
Answer: 885
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?
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?
6 minutes
Answer:
Area of Triangle ABC
is 9 square units