Maths Week in St.Paul s

Transcription

1 Maths Week in St.Paul s To enter read and solve the Problem Solving Questions found below Provide us with your answers on the answer sheet found at the end of this document (print and submit only page 11) Deadline for entry is Monday the 23 rd at 1:15 and entries can be submitted into the entry box found at the reception of the school The winner will receive a 20 One-for-All Voucher

2 Problem Solving Questions

3 1. The Joker has captured Batman. He has locked him in a room with three light switches. Each switch is connected to a bulb in another locked room. Three switches. Three bulbs. One fiendish puzzle. The Dark Knight has one hour to play with the switches before the Joker s brightly attired henchmen return, dragging him from the switch room into the bulb room. If he cannot then tell them which switch controls which bulb, the game is up, our hero will be killed and the Gotham City will be at the mercy of the cackling criminal. Can the Caped Crusader survive this prickly predicament? Will he live to save Gotham, or is the joke on him? Tune in next week, same bat time, same bat channel! How will Batman decide which bulb is attached to which switch?

4 2. The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits. Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them. "Upon each of your heads I have placed a hat. Now you are wearing either a blue hat or a white hat. All I will tell you is this- at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. However, you may be certain that there are not three white hats. I will shortly remove your blindfolds, and the test will begin. The first to correctly announce the colour of his hat shall be my advisor. Be warned however, he who guesses wrongly shall be beheaded. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom." With that, the king uncovered the sages' eyes, sat in the corner, and waited. One sage looked around and saw that his competitors each were wearing blue hats. From the look in their eyes, he could see their thoughts were the same as his, "What is the colour of my hat?" For what seemed like hours, no one spoke. Finally, he stood up and said, "The colour of the hat I am wearing is..."

5 3. In India, lilies grow extremely quickly. In one pond, a lily grew so fast that each day it covered a surface double that which it covered the day before. At the end of thirty days, it covered the whole pond. How long would it take two water lilies of the same type to cover the whole pond?

6 4. What is the next element in this sequence: 1, 11, 21, 1211, ,? 5. Write out the full name of the number 1,000,000,000,000,000,000

7 6. Place 10 dishes along the 4 edges of a table so that each edge has the same amount of dishes. Imagine the rectangle below is a table.

8 7. In the following problems, each group of lettered statements includes EXACTLY ONE false statement, and the rest are true. i. I am thinking of a number. Which one of these statements is false? A. The last digit is 1. B. The number is divisible by 3. C. The sum of its digits is 6. D. The number is prime. ii. Variables a, b, c and d represent integers. Which one of these equations is false? A. a = 9c B. b = c + 7 C. a = b + 1 D. c = b 4

9 8. Anita is baking a cake today. She bakes a cake every fifth day. How many days will it be before she next bakes a cake on a Thursday?

10 9. I m thinking of a two digit number. My number is special because adding the sum of its digits to the product of its digits gives me my original number. Can you discover my number?

11 10.

12 Maths Week Problem Solving Questions Answer Sheet Q1. Q2. Q3. Q4. Q5. Q6. Q7. Q8. Q9. Q10.

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