Random Puzzles 

Workings

Hint
In each word, exactly one letter is wrong.

Answer
I like bees. When I see a bee, it makes me think of the honey that they make. Honey makes my toast nice.

Workings

Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.

Answer
23,475.

Reasoning
By (1), the first digit is prime:
   2----
   3----
   5----
   7----

By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
   2-4--
   3-6--

By (4), the fourth digit is the third digit plus three:
   2-47-
   3-69-

By (5) the fifth digit is the difference between the first digit and the fourth digit:
   2-475
   3-696

We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
   23475

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
The word APRIL appears 34 times.

Answer
The word APRIL appears 34 times.