Random Puzzles 

Workings

Hint
Each line adds to 14.

Answer
 

Workings

Hint
The word MAY appears 39 times.

Answer
The word MAY appears 39 times.

Workings

Hint
There are 13 loaves in a baker's dozen.

Answer
Loaves in a dozen baker's dozen.

Reasoning
A baker's dozen is 13, so a dozen baker's dozen is:

   12 x 13 = 156 loaves

There are 15 red balls in snooker, and each of these can be followed by the black ball, and then the colours in order gives:

   15 x (1 + 7) + 2 + 3 + 4 + 5 + 6 + 7 = 147 points

This can rise to 155 if the break follows a foul.

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.