32 nd Annual Armstrong Atlantic State University High School Math Tournament Ciphering Round

Question 1 Make the statement true by filling in the boxes using each of the four symbols exactly once: =

Question 2 Suppose that the 4×4 array below is completed so that each row and each column is a permutation of the numbers: 1, 2, 3, 4. What is a – b? a 4 b

Question 3

Question 4 Two distinct numbers (a and b) are randomly selected from the set {2, 3, 4, 5, 6, 7, 8, 9}. (express answer as a fraction in simplest terms)

Question 5 A robot is programmed to do the following in a coordinate system: Its first move -- Start at the origin facing in the positive y direction and move one unit. Each subsequent move -- it is to turn 90 degrees clockwise and go forward 1 unit further than it went in the previous move. What is the sum of the coordinates of the robot after it completes its 10 th move?

Question 6 Each circle has a radius of 6 units. Consider the triangle formed by joining the three centers of the tangent circles. What is the area inside the triangle but outside the circles?

Question 7 What is the 110 th term of the sequence given below, where the terms are found by adding consecutive odd integers to previous terms? 0, 3, 8, 15, 24, 35, 48, 63, …

Question 8 A five digit number is created by using each of the digits 3, 4, 5, 7, and 8 exactly once. What is the probability that the number created will be a multiple of 4? (express answer as a fraction in simplest terms)

Question 9 A plane passes through a sphere, and the area of the circle formed by that intersection is 25π cm 2. The perpendicular distance from the center of the sphere to the plane is 12 cm. What is the length of the radius of the sphere?

Question 10 “Name five two-digit numbers that are evenly spaced out — like 32, 34, 36, 38 and 40 — in which all 10 digits from 0 to 9 are used once each. What numbers are these?” List 2 out of the 4 possible solutions. (As heard on NPR-Weekend Edition Sunday, December 13, 2009)