Riddles

1. Triangle sides are:   8x-93, 3x-31, 68-4x.  Find two solutions in whole numbers, and explain why they are the only ones possible.

2. A spider's kingdom is on the surface of a box hanging from the ceiling, with dimensions 7x5x4 metres. It sits in the middle of one of the largest sides. Find the shortest path from the spider to an unsuspecting fly, anywhere on the surface of the cube. Explain the logic of your solution.

3. Seemingly tough algebra:

4. Find the Greatest Common Denominator of these numbers: 221149, 17653, 33221, 64913.

5. Find area of D.

6. 

7.   a) Find a lowest denominator fraction in the range [235/164 , 225/157].

      b) Come up with an algorithm to find a lowest denominator fraction in a given range.

       Hint: Continued Fractions.

Reemon's riddles

1. Find the number of cubes that put together can both tile a square and construct a cube.

2. Find the number of squares that tile both a square and all surfaces of a cube.

Remarks: Remember that to all mathematical questions there are several possible replies:

* One set of solutions

* Infinite set of solutions

* No solution

* I don't know!