1. For problems 1 & 2, you are given four 'squares' of numbers for each problem. The same mathematical function(s) are applied to each square in each problem, but problems 1 & 2 each use different functions. One of the numbers in the last square in each problem has been replaced with a ?, & you must determine what number should be there instead.```7 3 8 8 5 0 6 ? 6 3 4 2 6 4 9 5 ``` Answer 2.```2 7 0 3 0 11 2 ? 8 9 5 6 10 11 4 3``` Answer HELLO, GOODBYE! 3. 12 members were present at a board meeting. Each member shook hands with all of the other members before & after the meeting. How many hand shakes were there? Answer PROBABILITY UNIVERSITY 4. At Probability University, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award. What percent chance is there that it will be a junior? Round to the nearest whole percent. Answer A DOZEN EDGES 5. If you take a marker & start from a corner on a cube, what is the maximum number of edges you can trace across if you never trace across the same edge twice, never remove the marker from the cube, & never trace anywhere on the cube, except for the corners & edges? Answer TWO & THREE 6. A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have 2 of their sides painted black? Answer FOLD IN HALF 7. If you started a business in which you earned \$1 on the first day, \$3 on the second day, \$5 on the third day, \$7 on the fourth day, & so on, how much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)? Answer PAY RAISE/PAY CUT 8. A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now her salary is \$22702.68. What was her salary to begin with? Answer 9. Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another). Answer 10. If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set:``` 21 5 28 13 16 2 24 30 ? 17 7 25 7 10 8 ``` Answer 11. You have 1,432 feet of fence that must be strung out in a straight line. A fence post must be placed for every 4 feet of fence, so how many fence posts will be needed? Answer 12. If each letter in the following equations represents a number from 1 through 9, determine what number each letter represents. A. A+A+B+C = 13 B. A+B+C+D = 14 C. B+B+C+D = 13 Answer 13. Anyone telesent (like being teleported or "beamed up") to Space Station Exray will arrive in pod A, B, or C. You are twice as likely to arrive in pod A than in pod B, & three times as likely to arrive in pod B than pod C. How likely is it that you will arrive in pods B, C, & A, in that order, the only three times that you are telesent to Space Station Exray? You may express your answer as a fraction or as a percentage. Answer 14. In a perfectly circular arena, I walk from the edge directly to the center. I then turn directly to my left, & walk in a straight line to the edge of the arena. I then turn to the right & follow along the edge for a total of 500 meters until I arrive at the point that I started from. What is the circumference of the inner edge of the arena? Answer 15. If 7 web programmers can format 1001 puzzles in 429 minutes, how long does it take 3 web programmers to format those 1001 puzzles? Answer 16. If you have 3 dice that are shaped as a tetrahedron, a cube, & an icosahedron, & you rolled each of them, each die would display a number from 1-4, 1-6, & 1-20, respectively. Assume that the tetrahedron & icosahedron are regular. If there is an equal chance that a die will display any of its numbers each time it is rolled, what percent chance is there that the numbers rolled will total 7 if all three dice are rolled once, & the numbers they display are added together? Answer 17. What are the maximum of separate volumes that can be formed by 2 interpenetrating cubes? a) Use only the surfaces of the cubes for consideration of the bounded volumes. b) Do not consider any subdivisions of the volumes. Answer 18. Andy, Bart, and Chris are eating at Smiley's All You Can Eat Pizza Buffet. Andy made 2.4 times as many trips to the buffet as Bart, and Bart made 6 fewer trips than Chris. What is the smallest possible total number of trips the 3 made to the buffet, assuming that each person made at least one trip? Answer CURRENT EVENT 19. In training for a competition, you find that swimming downstream (with the current) in a river, you can swim 2 miles in 40 minutes, & upstream (against the current), you can swim 2 miles in 60 minutes. How long would it take you to swim a mile in still water? Answer BUSINESS PSYCHOLOGY 20. All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors, & 62% are business majors. If there are 200 students, how many of them are majoring in both psychology & business? Answer