Emmy Noether - Circle 1 for 2006-2007€¦ · Emmy Noether – Circle 1 for 2006-2007 Emmy Noether...
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Emmy Noether – Circle 1 for 2006-2007 Emmy Noether - Circle 1 for 2006-2007 Part I: Problems Problem 1 In the Grade 6 Students’ 100 metre hurdle event, there are 10 hurdles. The first hurdle is 13 metres from the starting line. Consecutive hurdles are 8 metres apart. How far is the tenth hurdle from the finish line? (Note: ‘consecutive’ means one right after the other.) Extension : In an 80 metre hurdle race, the distances between hurdles are equal, the first hurdle is 12 metres from the starting line, and the last hurdle is 12 metres from the finish line. If there are 8 hurdles in all, how far apart are consecutive hurdles? Problem 2 The area of one side of an Emmy-Os single-serving cereal box is 96 cm 2 . The area of another side of the same box is 48 cm 2 . The area of the top of the box is 32 cm 2 . What is the volume of the box if the length of each edge is a whole number? Problem 3 A 12-hour digital clock displays palindromic numbers many times each day (e.g., 1:01, 1:11, 2:32, ...). a) What is the least length of time between two con- secutive such numbers? b) What is the greatest length of time between two consecutive such numbers? Extension : Is the answer to question b) the same for a 24-hour clock? Page 1 Part I – For the Student
Transcript of Emmy Noether - Circle 1 for 2006-2007€¦ · Emmy Noether – Circle 1 for 2006-2007 Emmy Noether...
Emmy Noether – Circle 1 for 2006-2007
Emmy Noether - Circle 1 for 2006-2007
2007
2006
Part I: Problems
Problem 1
In the Grade 6 Students’ 100 metre hurdle event, there are 10hurdles. The first hurdle is 13 metres from the starting line.Consecutive hurdles are 8 metres apart. How far is the tenthhurdle from the finish line? (Note: ‘consecutive’ means one rightafter the other.)
Extension:In an 80 metre hurdle race, the distances between hurdles are equal, the first hurdle is 12 metresfrom the starting line, and the last hurdle is 12 metres from the finish line. If there are 8 hurdles inall, how far apart are consecutive hurdles?
Problem 2
The area of one side of an Emmy-Os single-serving cereal box is 96 cm2.The area of another side of the same box is 48 cm2. The area of the topof the box is 32 cm2. What is the volume of the box if the length ofeach edge is a whole number?
Problem 3
A 12-hour digital clock displays palindromic numbers many times each day (e.g., 1:01, 1:11, 2:32,. . .).
a) What is the least length of time between two con-secutive such numbers?
b) What is the greatest length of time between twoconsecutive such numbers?
Extension:Is the answer to question b) the same for a 24-hour clock?
Page 1 Part I – For the Student
Emmy Noether – Circle 1 for 2006-2007
Problem 4
Freddy felt that Friday the 13th was very bad luck. He was somewhat consoled by his belief thatthere could be only one Friday the 13th in a calendar year, until his buddy Hakim told him therecould be two.
a) Was Hakim right? Explain how you know.
b) Could there be more than two Friday the 13ths?
July 2004
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December 2005
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Extension:Does there have to be at least one Friday the 13th in any given year?
Page 2 Part I – For the Student
Emmy Noether – Circle 1 for 2006-2007
Problem 5
Reena is making cubes for a game in which the cubes are selected froma bag. She has red paint and blue paint. She paints each face of a cubeeither red or blue. How many different cubes can Reena make? (Twocubes are not considered different if one can be rotated to match theother.)
Extension:Suppose Reena makes one face yellow. Could she make at least 10 different cubes with the remainingfaces each painted either red or blue?
Problem 6
100 Challenges (Suggested for groups of 2 to 4 students)
For this game, form teams (pairs or small groups); each team needs one die (or number cube)and a score sheet (below).
To play, first roll the die five times and place the resulting five numbers in the five boxes at thetop of the score sheet. The goal is to use these five numbers to form as many of the numbers from1 to 100 as you can, using adding, subtracting, multiplying, dividing, and combining digits. (e.g., a5 and a 2 could combine to form 52 or 25). Each number you form must use one or more of thesefive operations. None of the five digits rolled can be used more than once in forming a single number(unless you rolled two of that digit). For example, if you rolled 1, 2, 2, 5, 6, some of the numbers youcould form are 1 (2− 1), 2 (2× 1), 3 (5− 2), 4 (6− 2), 5 (5× 1), 6 (6× 1), 7 (5 + 2), 8 (5 + 2 + 1),12, 21, 25, 52, 65, 22, 60 (12 × 5), 28 (56 ÷ 2), 61(5 × 6 × 2 + 1), etc. As you form the numbers,write how you did it in the space beside that number on the chart. The team that forms the mostnumbers in a specified time wins the game. (A suitable time could be 20 or 30 minutes.)
Page 3 Part I – For the Student
Emmy Noether – Circle 1 for 2006-2007
SCORE SHEET FOR 100 CHALLENGES
= 1 = 2 = 3 = 4 = 5
= 6 = 7 = 8 = 9 = 10
= 11 = 12 = 13 = 14 = 15
= 16 = 17 = 18 = 19 = 20
= 21 = 22 = 23 = 24 = 25
= 26 = 27 = 28 = 29 = 30
= 31 = 32 = 33 = 34 = 35
= 36 = 37 = 38 = 39 = 40
= 41 = 42 = 43 = 44 = 45
= 46 = 47 = 48 = 49 = 50
= 51 = 52 = 53 = 54 = 55
= 56 = 57 = 58 = 59 = 60
= 61 = 62 = 63 = 64 = 65
= 66 = 67 = 68 = 69 = 70
= 71 = 72 = 73 = 74 = 75
= 76 = 77 = 78 = 79 = 80
= 81 = 82 = 83 = 84 = 85
= 86 = 87 = 88 = 89 = 90
= 91 = 92 = 93 = 94 = 95
= 96 = 97 = 98 = 99 = 100
Page 4 Part I – For the Student
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