Random Puzzles 

Workings

Hint
I bought at least 6 of each stamp.

Answer
Six lots of 4p, 7p, and 19p, and ten lots of 5p, and 12p.

Reasoning
For three denominations of stamps, I was asked to buy 6 of each, and for the other two denominations, I had to buy 10 of each.

So I had to buy at least 6 of all five denominations.

This would be for a total of 6 x (4 + 5 + 7 + 12 + 19) = 282p = £2.82.

The remaining 68p has to buy the remaining 8 stamps, 4 of each of the two remaining denominations.

If we just bought 1 of each of the two remaining denominations they would have cost 68 ÷ 4 = 17p.

So the two remaining denominations must have been 5p and 12p.

Double-Checking
 6 x  4 =  24
10 x  5 =  50
 6 x  7 =  42
10 x 12 = 120
 6 x 19 = 114

For a total of 24 + 50 + 42 + 120 + 114 = 350p = £3.50.

Workings

Hint
One word starts with T and the other with W.

Answer
Tower and wrote.

While captive in the tower, King James wrote an entire book.

Workings

Hint
Try to find Drew's boat colours first.

Answer
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Reasoning
By (3), Yellow and Blue went together (Combination1: Yellow + Blue).

By (4), Green and Blue went together (Combination2: Green + Blue).

By (2), Billie had Green. By (5), Charlie had Yellow. By (6), Drew had Blue. Giving:
Alex
Billie    Green
Charlie   Yellow
Drew      Blue

By (6), Drew had Blue, but not Green. This can't have been (Combination2: Green + Blue), so must have been (Combination1: Yellow + Blue):
Alex
Billie    Green
Charlie   Yellow
Drew      Blue    + Yellow

By (2), Billie didn't have Red, so Alex and Charlie must have had Red:
Alex      Red
Billie    Green
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Which means that Billie had (Combination2: Green + Blue), and Alex had Green:
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Workings

Hint
One of the cheeses is Cheddar.

Answer
Edam, Cheddar, Brie, Cheshire.