Random Puzzles 

Workings

Hint
Try reversing the numbers.

Answer
891.

If we reverse each of the numbers we get:

   203 202 201 200 199 ?

Which is counting down from 203, and the next number is 198, which is 891 when reversed.

Workings

Hint
Only the first letter is important.

Answer
3,000 miles.

Take the alphabetic position of the first letter, halve, and then multiply by 1000.

You could also multiply by 500 instead.

Double-Checking
F is the 6^th letter of the alphabet, halving gives 3, multiplying by 1000 gives 6000.

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
It depends on the length of the word.

Answer
2 buttons.

The number of buttons is 10, minus the length of the word.