Okay! I know you are ready to face the challenge, roll up your sleeves, sharpen your pencils and let’s go!
Rules:
You must complete this work on loose paper.
You must show all your work.
The paper must have a proper heading and the problem number listed on it.
All problems must be placed in the folder on Margaret’s desk by Friday of the week it is issued.
All problems will be scored 1-4.
Neatness and organization on the paper count!
You do not have to complete all of the problems to enter the weekly contest.
The ultimate challenge awards will be based on points, so the more problems you answer, the more points you will earn overall.
You do not have to enter problems each week.
Margaret has the final say in any dispute!!!!!!
This Week’s Problems
Due: Friday, February 4th
#1 Four girls, Anne, Beatrix, Cecilia, and Dori, sang songs at graduation last year. Every song was sung by three of them and the fourth girl accompanied them on the piano. Anne sang the most songs, a total of 8 of them. Dori sang the least, only five times. How many songs did the girls sing?
#2 “How many bananas did you bring?” – asked Judy from her Mom. Her mom said: ” A third of the bananas is 3 less than the half of them.” How many bananas did she bring home?
#3 When a sleeper woke up in the middle of the night and checked his clock, it showed 3 o’clock, but it was stopped. He started the clock again and went back to sleep. When he woke up in the morning a nearby tower clock was tolling seven times. He checked his clock, but it showed 6 o’clock. What time was it when he woke up at night?
Last Weeks Problems
Due: Friday, January 28, 2011
#1: The oldest of three brothers is 14 years older than the youngest. The one in the middle is 4 years younger than the oldest one. Everybody’s age is a prime number. How old are they?
#2: Three defendants stand in front of a judge. Every one of them answers 3 questions, partially with a lie (each person lies at least once and at most twice):
The answers of A: “It was B.” “I have never been on the scene.” “I am innocent.”
The answers of B: “C is innocent.” “I did not do it.” “All what A says is a lie.”
The answers of C: “It wasn’t me.” “A is lying when he says that he has never been on the scene.” “B is lying when he says that all what A says is a lie.”
Find out who is guilty.
#3 Four girls participate in a running race. After the race they were asked what place they finished on.
Anna: “I was neither first nor last.”
Bella: “I was not the first at the finish line.”
Cecilia: “I was first.”
Dory: “I was last.”
Somebody, who saw the race, said: “Three of the four answers are true, and one is false.”
Who was the first, and who made the false statement?
Due: Friday, December 3, 2010
10.16
How many times does each digit 0-9 appear in a list of all whole numbers from 0 to 100 inclusive? In other words, if your wrote the whole numbers 0 – 100 on a piece of paper, how many times will the digit 0 be written, how many times will the digit 1 be written, how many times will the digit 2 be written, etc.
10.17
Your teacher wants to give pieces of chocolate candy to students in your class. The teacher has bags of chocolate candy each with less than 100 pieces inside each bag. If your teacher makes groups with 2, 3, or 4 pieces of candy she will have 1 piece left over from the bag. If she makes groups with 5 pieces of candy, she will have none left over. If each bag has the same number of pieces, how many pieces of candy could be in each bag? By the way, there may be more than one answer. Please provide all possibilities.
10.18
What is the 200th letter in the following pattern:
ABBCCCDDDDEEEEE…?
Due: Friday, November 19, 2010
10.13
Carly and Cassidy spent $207 on a shopping spree. One item they purchased cost $1. All other prices were prime numbers (dollars only) and each digit (1 through 9) was used once and only once. The digits of one item summed to 7. What was the value of each item?
Answer = $1, $2, $5, $3, $67, $89
10.14
Your school opens one hour before school begins. Students arrive in groups. You and your brother are the first two students to arrive so the two of you are considered the first group. The second group to arrive has 1 more student than your group. The third group has one more student than the second group. If there are 405 kids at your school on this day, how many groups will arrive at school, assuming they all meet the requirement of having one more member than the previous group before them?
Answer = 27 groups
10.15
A unit fraction is a fraction in the form of 1/n where n is a positive integer. The difference between two unit fractions is 1/72. Find the two unit fractions.
Answer = 1/8 – 1/9 = 1/72
Past Problems
Due: Friday, November 12, 2010
10.10
If you were to construct a 8 × 8 checkered square (i.e., a 8 × 8 chessboard), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.
Answer = 1296
10.11
Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 6 of his balls they would have an equal number; but, if Glenn would give Jason 6 of his balls, Jason would have 4 times as many balls as Glenn. How many balls does Jason have?
Answer = 26
10.12
It was vacation time, and so I decided to visit my cousin’s home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long.
Now, there were 7 mornings when we did nothing, 11 evenings when we stayed at home, and a total of 10 days when we jogged or played tennis. For how many days did I stay at my cousin’s place?
Answer = 14
Due: Thursday, November 4, 2010
Problem 10.7
840 stickers were given to 42 children. 2/3 of the children were boys, and each of them received the same number of stickers. Each girl received twice as many stickers as each boy. How many stickers did each girl receive?
Answer = 5 stickers
Problem 10.8
Soo-Jin and Mary had an equal number of beads. After Soo-Jin gave 54 beads to Mary, Mary had 7 times as many beads as Soo-Jin. How many beads did they have altogether?
Answer = 144 beads
Problem 10.9
Antonio and Abby had the same number of paperclips. After Antonio gave 30 paperclips to Abby, Abby had twice as many paperclips as Antonio. How many paperclips did they have in all?
Answer = 180 paperclips
Due: Friday, October 29, 2010
Problem 10.4
Lauren saved $84 more than Fiona. 1/5 of Lauren’s savings was the same as 3/8 of Fiona’s savings. How much did Lauren and Fiona save together?
Answer = $276
Problem 10.5
Logan and Izzy had the same number of stickers. After Izzy gave him 72 stickers, Logan had 3 times as many stickers as Izzy. How many stickers did they have altogether?
Answer = 288 stickers
Problem 10.6
David and Amrita had an equal number of marbles. After Amrita gave 50 marbles to David, he had 5 times as many marbles as her. Find the total number of marbles they had.
Answer = 150 marbles
Due: Friday, October 22, 2010
Good Luck!!! Think, they are not as hard as they look!!
Problem 10.1
2 diamond rings and 4 silver rings cost $1,440. A diamond ring and a silver ring cost $660. How much does a silver ring cost?
Answer
$60.
Problem 10.2
Alex spent 3/7 of his money. He gave 1/4 of the remainder to his sister. He had $120 left. How much money did he have in the beginning?
Answer
$280.
Problem 10.3
Julio is 36 years old, and James is 11 years old. In how many years will Julio’s age be twice James’s age?
Answer
14 years