Australian Maths Competition

Hey,

I'm in Year 10, does anybody know the answers to the last 5 questions?

All I know:

The question that asks "how many numbers under 2010 have 3 factors" is 14.

Also, it would be nice if you can post what the question was, only if you can though :)

Cheers,

EDIT:

So far we have:

Question 26. how many numbers under 2010 have 3 factors

A. 14

Question 27. Two 10*18*L blocks are placed on either side of a cylinder of length L to stop it from rolling. One block has 10*L face on the ground while the other block has an 18*L face on the ground. The block on the left sticks out 4 units more than the one on the right.

What is the radius of the cylinder?

A. 25

Question 28. A 3-digit number is subtracted from a 4-digit number and the result is a 3-digit number.

□□□□-□□□=□□□

The 10digits are all different.

What is the smallest possible result?

A. 246

Question 29. I have a list of thirty numbers where the first number is 1, the last number is 30 and each of the other numbers is on more than the average of its two neighbours. what is the largest number in the list?

A. 226

Question 30. There are so many towns on the island of Tetra, all connected by roads. Reach town has three roads leading to three other different towns: one red road, one yellow road and one blue road, where no two roads meet other than at towns. If you start from any town and travel along red and yellow roads alternately (RYRY...) you will get back to your starting town after having travelled over six different roads. In fact RYRYRY will always get you back to where you started. In the same way, going along yellow and blue roads alternately will always get you back to the starting point after travelling along six different roads (YBYBYB). On the other hand, going along red and blue roads alternately will always get you back to the starting point after travelling along four different roads (RBRB). How many towns are there on Tetra?

A. 24