Random Puzzles 

Workings

Hint
This is a well-known sequence.

Answer
R.

Reasoning
The last letter of September.
y = January
y = February
h = March
l = April
y = May
e = June
y = July
t = August
r = September

Workings

Hint
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer − 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+ 1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73, and this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.

Workings

Hint
Calendar.

Answer
Dragon.

From the Chinese calendar in reverse order.

Workings

Hint
Think of the phrase 'my bucket and spade'.

Answer
In the phrase 'my bucket and your spade', the gap between 'my' and 'and' is the same as the gap between 'and' and 'spade', namely one word.

Indeed, this logic can be continued to give the following sentence. In the first sentence the gap between 'and and' and 'and and' is seven words, et cetera.