Otago Problem Solving

Answer in the comments box or email me fionabester@ashgrove.school.nz

Problem 1

Kirsty's school locker has a two-digit number on it. The sum of the two digits is 10 and their difference is 2. If the locker number is less than 50, what number is it?

Problem 2

When Louise put 25 golf balls in her bag, it was 1/2 full. When Matt put 17 golf balls in his bag, it was 1/3 full. When Nick put 12 golf balls in his bag, it was 1/4 full.

Who had the largest bag?

Problem 3

The pictures below show how matches can be used to make triangular shapes that have one, two and three matches along a side. 
How many matches are needed to make a triangular shape of the same pattern, which has 6 matches along one side?

Problem 4

One rectangular wall of Bob's house contains a door and a window. Bob wants to paint this wall, but not the door (nor the window!). The wall is 7 m by 3 m, the door is 2 m by 1 m, and the window is 2 m by 1.5 m. If each can of paint covers 4 sq m, how many cans should Bob buy for one coat of paint?

Problem 5

Tina's house and her school are on the corners of square blocks as shown. The shortest distance from her house to the school is along the sides of 5 blocks. Two such paths are shown.
How many different paths are there of this length from Tina's house to her school (including the two paths shown)?