### Fibs

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

### Hallway Borders

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

### Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

# Cakes and Buns

##### Stage: 3 Short Challenge Level:
One cake and one bun cost a total of 62p. Note that 512 = 8 x 62 + 16, and note also that 16 = 39 - 23. Hence

512 = 8(39 + 23) + 16 = 8(39 + 23) + 39 - 23 = 9 x 39 + 7 x 23.

As 39 and 23 do not have a common factor other than 1, Helen must have bought 9 cakes and 7 buns.

This problem is taken from the UKMT Mathematical Challenges.
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