Random Puzzles 

Workings

Hint
Look at the piece by Bach, and the single.

Answer
Composer   Format  Length
Beethoven  album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9

Reasoning
By (1), the piece by Bach lasts 8 minutes. By (3), the single lasts 7 minutes.
Composer   Format  Length
                   6
           single  7
Bach               8
                   9

By (4), the piece by Butler is on the DAT tape. But, by (2), this can't be the shortest, so it must be 9 minutes long.
Composer   Format  Length
                   6
           single  7
Bach               8
Butler     DAT     9

By (1), the CD can't be the shortest, so must be 8 minutes long.
Composer   Format  Length
                   6
           single  7
Bach       CD      8
Butler     DAT     9

The album must therefore be 6 minutes long, and by (3) doesn't contain any Holst.
Composer   Format  Length
           album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9

Which means that the album was the piece by Beethoven.
Composer   Format  Length
Beethoven  album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter which has a problem with the middle row of letters – they 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
How many pieces on the top layer had two sides with icing?

Answer
15 pieces.

Reasoning
On each layer there are 4 pieces with exactly two sides of icing.

Therefore Kevin ate 12 pieces, leaving 15 for the guests.

Workings

Hint
Think literally.

Answer
Incorrectly!