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
How many clock minutes pass in a real hour?

Answer
1:20pm.

Reasoning
The clock now shows 10:12am, so we know that 10 x 60 + 12 = 612 clock minutes have passed.

Since the clock is losing 6 minutes every hour, for every real hour that has passed, the clock will show 54 minutes.

So, 612 ÷ 54 ≈ 11.33 real hours have passed.

This equals 680 minutes, which is 11 hours and 20 minutes = 11:20am.

The clock stopped 2 hours ago, therefore the time must now be 1:20pm.

Workings

Hint
The first two words begin with A and S.

Answer
Actions speak louder than words.

Workings

Hint
Start by looking at the 6 and 4 on the top row.

Answer