Greetings Problem Solvers.

Due to Exam week at the high school and the small number of responses from the middle level grades, Problem of the Week will take a pause.

Problems from weeks #14, #15, and #16 will remain open for submitting solutions until 3:00 pm Friday, February 1st.

Problem # 17 will be posted by Monday, February 4th.

Problem of the Week # 16: January 21st, 2008
Submit your solutions by Friday, January 25th, 2008 to
tubbsjac@nbed.nb.ca

Grade 6

A sixth grade class has 35 students out of which 25 are girls. There are 12 students in the class who wear glasses. In this class there are 7 boys with no glasses. How many girls wear glasses in this class?

Grade 7: Mean Missing Number
The mean of a set of five numbers is known to be 9.4. If four of the numbers in the set are 7, 11, 15, and 19, what is the missing number?

Grade 8
We have the following information about a 4-digit number: it is odd; every one of its digits is smaller than 7; its digits are in a decreasing order from left to right; every sum of its two consecutive digits is odd; it is divisible by 3 and 7. Find this number.
Grade 9: Rapid Growth Problem
1, 5, 14, 30, 55, 91, 140, ___, ___, [ ___ ]
Determine the third number in the above pattern.

Grade 10: Picky Numbers
A number is called a "Picky Number" if it is a positive integer and the preceding and succeeding whole numbers are prime. In other words, 4 is a "Picky Number" since it is a positive integer and both 3 and 5 are prime numbers. Find the average (mean) of all "Picky Numbers" less than 100.

Problem of the Week #15: Posted January 13, 2008

Grade 6
A farmer was selling his produce at the market. He had 50 small baskets with 3 tomatoes in each basket. By the end of the first day he had sold half of his tomatoes. If he sold 7 baskets of tomatoes the following day, how many tomatoes would he have left?

Grade 7
Find a number such that when added to the numerator and denominator of 2/11, the resulting fraction is equivalent to 1/2.

Grade 8
The number 75 can be expressed as the sum of consecutive whole numbers. For example, 13 + 14 + 15 + 16 + 17 = 75 and 10 + 11 + 12 + 13 + 14 + 15 = 75. Find one other set of consecutive whole numbers that sum to seventy-five.

Grade 9
Tom and Rachel each have a collection of coins consisting only of pennies, nickels, dimes, and quarters. Both collections have the same cash value, but they have different numbers of each type of coin. In particular, Rachel has four more quarters than does Tom, but Tom has more of every other type of coin. In fact, Tom has a total of 32 more coins than does Rachel. If Rachel has 23 nickels, how many nickels does Tom have?

Grade 10
A circle is circumscribed around both a square of area 5 and a rectangle of area 4. Find the dimensions of the rectangle.

Happy New Year. Please note that Problem #13 and #14 are both open this week. There were no correct submissions for #13 before the Christmas Break.

Problem of the Week: # 14 January 7 -11, 2008

Grade 6
Teri thought of a positive whole number. She told me that it has 12 positive divisors, including 6 and 25. What is Teri's number?

Grade 7
A village wants to build a 1500 metre-pedestrian walk for which they have $62 500. One metre of asphalt-covered walkway costs $36, while one metre of tiled walkway costs $53. The village wants to tile as much of the walkway as they can afford. How many metres will be covered with tiles and how many metres with asphalt?

Grade 8
The sum of the squares of the digits of a positive two digit whole number is 50. Find all of these numbers. (There is more than one)

Grade 9
Two regular polygons have a combined total of 17 sides and 53 diagonals. How many sides does each polygon have? [Hint check the diagonal rule from grade 8]

Grade 10
Aisle Seats
Seven people watching a play are sitting in a row that contains seven seats. After intermission, they return to the same row but choose seats randomly. What is the probability that neither of the people sitting in the two aisle seats was previously sitting in an aisle seat?