Random Puzzles 

Workings

Hint
How many squares of size 1 x 1 are there?

Answer
There are 116 squares without a rook.

Reasoning
There are 61 squares of size 1 x 1.
There are 37 squares of size 2 x 2.
There are 15 squares of size 3 x 3.
There are  3 squares of size 4 x 4.

Giving a total of 61 + 37 + 15 + 3 = 116 squares.

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter which has a problem with the middle row of letters, which print spaces instead. The letter should have read:
Dear Sir,

I recently visited one of your outlets to buy one of your typewriters. However, as you can see I am having a small problem.

The middle row of the keyboard appears to be faulty.

I would be very grateful if you could despatch a replacement by return post. Failing this, could you please send an engineer to resolve this problem as a matter of urgency.

Yours faithfully,

Mrs Middins.

Workings

Hint
Start by looking (2).

Answer
Ashley crossed first.

They crossed in the following order (first is on the right):

Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.

Reasoning
Starting with (2), we can place Ray, Emery, Logan, and Riley as follows:

   Riley, -, -, Logan, -, Emery, -, Ray, -

(6) tells us that Taylor got on just after Emery, giving us:

   Riley, -, -, Logan, Taylor, Emery, -, Ray, -

(5) tells us that Jessie got on two people before Taylor, giving us:

   Riley, -, -, Logan, Taylor, Emery, Jessie, Ray, -

By (1), Chris got on two people after Logan, giving us:

   Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And (1) also tells us about Sam, giving:

   Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

We now have a line of 11 people, the missing person is either in front of Ray, or behind Sam.

The only way to place Alex, Quinn, and Billie using (3) and (4) is if the missing person is behind Sam giving:

   -, Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And therefore we can now place Alex, Quinn, and Billie as follows:

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, -

But who crossed first?

The only person we've not yet found a space for is Ashley. So Ashley crossed first.

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.

Workings

Hint
The first country is Bangladesh.

Answer
Bangladesh, Egypt, Fiji, Finland, Japan, Liechtenstein, Nicaragua, Switzerland, Tunisia, Zambia.