WASHINGTON STATE MATHEMATICS COUNCIL 1999 MIDDLE SCHOOL MATH OLYMPIAD EIGHTH GRADE ALGEBRAIC SENSE Make sure you include proper units in your answer! 8

1. A gray squirrel has 65 nuts gathered in its nest, and a red squirrel has 114 nuts gathered in its nest. A wily woodpecker steals nuts from both squirrels' nests. It steals 2/3 as many nuts from the nest of the gray squirrel as it steals from the nest of the red squirrel. After the woodpecker takes the nuts from both nests, the red squirrel has twice as many nuts left as the gray squirrel has. How many nuts does the gray squirrel have left?

 2 How many intersections of two or three line segments are there on the surface of cube at right? [Note: The cube is a 4-inch cube. The segments are all spaced 1 inch apart.]

3. A number is increased by 25%. The resulting number is decreased by 16%. The result is 1 more than the original number. What is the original number?

 4 How many dots would there be in the twentieth figure in the sequence at right?

 5 The input and output of a number changing machine are shown at right. For each input number on the left, the output number on the right is generated. What output number would be generated if the number "n" were the input number? Write your answer in terms of n. Input 4 16 40 Output  4 52 148