Random Puzzles 

Workings

Hint
Try to find out where Mrs Umbrella lives first.

Answer
From, left to right:
#1 Mrs Scott    - glass
#2 Mrs Umbrella - straw
#3 Mr Tidsley   - brick
#4 Mr Wilshaw   - wood

Reasoning
If we separate and label the clues, and label the bungalows #1, #2, #3, #4 from left to right we can see that:
Mrs Scott's bungalow is somewhere to the left of the wooden one. The third one along is brick. Mrs Umbrella owns a straw bungalow Mr Tidsley does not live at either end. Mr Tidsley lives somewhere to the right of the glass bungalow. Mr Wilshaw lives in the fourth bungalow. The first bungalow is not made from straw.
By (6) Mr Wilshaw lives in the fourth bungalow.
   #1
   #2
   #3
   #4 Mr Wilshaw

By (3), Mrs Umbrella owns the straw bungalow. By (7) it isn't #1, by (2) it isn't #3, so it must be #2.
   #1
   #2 Mrs Umbrella - straw
   #3
   #4 Mr Wilshaw

By (4), Mr Tidsley must therefore live in #3, which, by (2) is the brick bungalow.
   #1
   #2 Mrs Umbrella - straw
   #3 Mr Tidsley   - brick
   #4 Mr Wilshaw

By (1), Mrs Scott's bungalow must be #1, and #4 must be the wooden one.
   #1 Mrs Scott
   #2 Mrs Umbrella - straw
   #3 Mr Tidsley   - brick
   #4 Mr Wilshaw   - wood

This leaves #1 as the glass bungalow.
   #1 Mrs Scott    - glass
   #2 Mrs Umbrella - straw
   #3 Mr Tidsley   - brick
   #4 Mr Wilshaw   - wood

Workings

Hint
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

Answer
35 birds, 5 mice, and 10 cockroaches.

Reasoning
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

We can write down expressions for the heads and the feet – calling birds B, mice M, and cockroaches C.

Counting the heads:
(1)    B +  M +  C =  50

Counting the feet:
(2)   2B + 4M + 6C = 150

We are told that for every mouse there are two cockroaches so, C = 2M. Update (1) and (2) to give:
(3)    B +  3M =  50
(4)   2B + 16M = 150

If we double (3) we get:
(5)   2B +  6M = 100

We can now do (4) – (5) to give:
 10M = 50
   M = 5

So, we have 5 mice (and 10 cockroaches).

We can use M = 5 in (3) to give:
 B + 3 x 5 = 50
    B + 15 = 50
         B = 35

So, C = 10, M = 5 and B = 35.

Double-Checking
10 cockroaches have 10 heads and 60 feet.
5 mice have 5 heads and 20 feet.
35 birds have 35 heads and 70 feet.

The total number of heads = 10 + 5 + 35 = 50.

The total number of feet = 60 + 20 + 70 = 150.

Workings

Hint
Think of chickens.

Answer
Don't count your chickens until they're hatched.

Workings

Hint
A little bit of algebra might help.

Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.

Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:

   ⁵/₈ x (12 x A + B) = (12 x B + A)

Simplifying gives:

   A = ⁹¹/₅₂ x B

As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.

B = 4 is the only possible value, which means that A = 7.

So I originally asked for 7 feet, 4 inches.

Double-Checking
I received 4 feet, 7 inches = 55 inches.

I asked for 7 feet, 4 inches = 88 inches, and 88 x ⁵/₈ = 55.