CSE Day 2016 COMPUTE Exam. Time: You will have 50 minutes to answer as many of the problems as you want to.

Transcription

1 CSE Day 2016 COMPUTE Exam Name: School: There are 21 multiple choice problems in this event. Time: You will have 50 minutes to answer as many of the problems as you want to. Scoring: You will get 4 points for each correct answer, 1 point for each unanswered question, and 0 points for each incorrect answer. You will be give credit for questions as correct. Thus there is a max score of 100 points on this event, and you would get 37 points if you turned in a blank answer sheet. This front page will be your answer sheet. You need to turn it in at the of the time. You may keep the contest problems. Answers: 1: 11: 21: 2: 12: 22: +4 3: 13: 23: +4 4: 14: 24: +4 5: 15: 25: +4 6: 16: 7: 17: 8: 18: 9: 19: 10: 20: 1

2 1 The cars A, B, C, D, E, F, G, H, I arrived at a toll station on a highway in the order listed, with A being first. They each pulled into one of the multiple booths available to pay their toll, not necessarily the first available one. When they leave they are observed to be in the following order G, E, A, I, C, H, B, F, D. What is the minimum number of toll booths that need to be open for this to occur? There are two kids, Sara and Karim. Sara has blue paint: B, and Karim has red paint: R. They have a sequence of 8 wooden blocks that start unpainted: U. They have also decided on a list (3, 7, 2). Karim and Sara have decided to paint these blocks by starting at di erent times and progressing at a rate of their individual choosing, individually removing the first number (n) from the list, and then proceeding to paint every nth block, starting from the first, their color. If they come to a block that the other individual is painting, they will wait until that individual is done, and then proceed to paint over the block with their color. Which of these options is not a possible outcome? UBRBURRB URBRUBRR UBBBUBRB URBRURBR UBRBUBBB 3 We want to completely fill the white space in this grid with squares that do not overlap. The squares can be of di erent sizes. What is the fewest number of squares that are needed to accomplish this? In number bases, you have di erent place values, and a range of numbers that can go into any of these places. In this number system, you can only use the digits 0 and 1. The place values are based upon the Fibonacci numbers: fib fib = fib fib fib A, B, and C neither A, B, C, nor D 2

3 5 In this puzzle, each row and each column must contain each of the numbers 1, 2, 3, 4. Further, when applying the operator printed in each bounded region to all the numbers you enter into the region, starting with the largest number and working to the smaller ones, the result must equal the value which is also printed in the region. (for example +9 would mean that the numbers in the bounded region, when added, equal 9.) What is the product of the numbers on the diagonal of the solution, starting in the upper left and going to the lower right corners? none of these 6 A hotel has an unusual way of numbering their rooms. The first digit of the room number is the floor and the second is it s position in the listing of that floors rooms by how far they are from the elevator. The hotel can represent all it s rooms as two digit numbers when following this system. The person at the front desk would like you to order the room keys so that the lower floors are before the upper floors as long as the distance to walk is not greater on the lower floors. What would be the proper order for these room keys? The current rooms available: None of the above. 7 There are 10 students in your schools AP Computer Science Principles class (Alexis, Becky, Carl, Dennis, Elise, Fred, Gina, Han, Imus, Janna). The girls in the class are (Alexis, Becky, Elise, Gina, Janna). The students who are taller than 5 are (Becky, Carl, Elise, Fred, Han). The students who are taking psychology are (Alexis, Becky, Dennis, Fred, Imus). Who are the Boys who are neither taller than 5 feet nor not taking psychology? (Carl, Elise, Gina, Han, Janna) (Dennis, Fred, Imus) (Dennis, Imus) (Carl, Han) None of the above are correct 3

4 8 A robot needs help getting out of a maze. Unfortunately, its memory is broken, and it can only remember three instructions. What set of instructions, if repeated lessly, would get the robot to the of the maze? Note that the robot starts on the start tile oriented in the direction of the arrow. When the robot moves right one or left one, it adjusts its orientation (i.e. it turns in the indicated direction, then moves forward). Start Stop Forward one, right one Forward one, right one, left one Forward two, right one Right one, forward one None of the above. 9 Which of the circuits below are logically equivalent? Use the above as reference. Circuits 1 & 2 Circuits 2 & 3 Circuits 1 & 3 All of the above None of the above 4

5 10 For any simple polygon (its edges do not intersect) with four or more vertices, you can add some line segments such that this polygon will be completely divided into triangles. One way of doing this, has these line segments have their points on vertices of the polygon. Using this method, which of the following statements is false? If the polygon has n vertices, this will create n - 2 triangles. If the polygon has n vertices, there can be at most n/2, rounded down, triangles with two sides shared with the polygon. If the polygon has n vertices, this will take exactly n - 3 vertices to fully accomplish. There must be at least two triangles, each with two sides that are shared with the polygon. Two of these statements are false. 11 In the two examples below that calculate the value of the nth Fibonacci number, what is the positive di erence in the number of times they print something out when Fibonacci(5) is called? Fibonacci(n) Fibonacci(n) print n array rememberfib // all zeroes if n apple1 rememberfib[0] = 1 return 1 rememberfib[1] = 1 else return FibonacciCompute(n) return Fibonacci(n-1) + Fibonacci(n-2) If FibonacciCompute(n) print n if(rememberfib[n] == 0) rememberfib[n] = FibonnaciCompute[n-1] + FibonacciCompute[n-2] If return rememberfib[n] You take your pencil and put it on a sheet of paper, move it around, and then return it to the place you started, without lifting it. What is the minimum number of colors it would take, for any such drawing, to color every closed space within the drawing such that no two spaces colored the same, share a boundary edge Noe of the above. 5

6 4 13 This is a 4x4 sudoku puzzle. Each row, column, and quadrant must have the digits 1, 2, 3, and 4 appearing exactly once. Find the sum of the values in the corners of the sudoku puzzle Suppose great(a,b) outputs the larger of the two values a, b, and less(a,b) outputs the lesser of the two values. Which of the following statements is true if great(great(a,b), great(less(b,c),e)) is evaluated? cwillneverbereturned It will always return the largest of a, b, c, or e B will always be returned if b a If b c, b will never be returned None of the above is correct 15 If you are not tricked by the problem and you can eliminate two options from the choices for a problem, then it benefits you to guess. Which of the following statements is equivalent to the previous statement? If doesn t benefit you to guess, you couldn t eliminate two options or were tricked If you did guess, you were tricked If you were not tricked but didn t guess, you eliminate two options If you were tricked, then you would benefit from guessing None of the above 6

7 16 Romeo and Juliet are on opposite s of the city and want to meet up. They can t let anyone see them, so they must travel through an underground tunnel system. Each dot marks an intersection in the tunnels, and the number by each connecting edge indicates how many minutes it takes to travel through the tunnel. What is the shortest amount of time possible for Romeo and Juliet to meet at the same intersection? 8minutes 10 minutes 11 minutes 7minutes 9minutes 17 If you know that these 3 statements are true for a line of people: 1) Sue is behind Mary. 2) Colin is directly in front of Nick. 3) Nick is 2 people behind Steve. Which of these statements could be true? Steve is in front of Mary. Colin is in front of Steve. Steve is behind Mary. A and C all of the above. 7

8 18 If a person were following these instructions, which of these necklaces would it not be possible to create? 19 A frog is trapped in a well. Each day, he manages to hop up two feet, but slides back a foot at night when he falls asleep. What gets printed when getout(6) is called? getout(depth) print depth-2 if(depth < 0) sleep(depth-2) If sleep(depth) getout(depth+1) print depth None of the above 8

9 20 An army of frogs with limited horizontal jumping ability is traversing a swamp, the path is narrow so they hop in a single file line. Occasionally a hole appears in the path. The holes are crossed in the following manner. 1. as many frogs that can fit jump into the hole 2. the rest of the army crosses 3. the frogs jump out of the hole The images on the right demonstrate this process. In what what order do the frogs find themselves in after they cross the third hole? None of the above 21 An oil company is asking to build a new pipeline. You have been asked to determine what the current maximum amount of oil, in a day, that they can s from their oil well to their refinery. You have been given a graph of their pipe network annotated with the amount of oil that can pass through each section in a day (in millions of barrels.)