Random Puzzles 

Workings

Hint
Cockroaches have 6 feet, mice have 4, and birds have 2. They all 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
Look at the first letters of the words.

Answer
Alphabet.

The first letters of the words are spelling BrainBashers.

Workings

Hint
Look to the skies for the answer.

Answer
S.

From Saturn.

Reasoning
These are the initial letters of the planets.
M = Mercury
V = Venus
E = Earth
M = Mars
J = Jupiter
S = Saturn

Workings

Hint
Look at the first letters of the three words.

Answer
Giraffe.

The initial letters of the words spell FROG.