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?