Medium Puzzles 

Workings

Hint
Start by looking at clue (5), and then at the first part of clue (6).

Answer
# Name   Wore  Colour
1 Gary   2     red
2 Larry  3     green
3 Barry  1     yellow
4 Harry  4     blue

Reasoning
By (5), the winner wore #2, and Harry finished last:
   # Name   Wore  Colour
   1        2
   2
   3
   4 Harry

By (6), the person who finished second wore green, and by (4), wore #3:
   # Name   Wore  Colour
   1        2
   2        3     green
   3
   4 Harry

By (1), only the person in last place could have worn the same number as the position they finished:
   # Name   Wore  Colour
   1        2
   2        3     green
   3        1
   4 Harry  4

By (3), Gary didn't wear green (so can't have finished second) and beat Barry (so can't have finished third), which means that he must have finished first.
   # Name   Wore  Colour
   1 Gary   2
   2        3     green
   3        1
   4 Harry  4

By (6), Barry wore yellow, so must have finished third:
   # Name   Wore  Colour
   1 Gary   2
   2        3     green
   3 Barry  1     yellow
   4 Harry  4

By (6) the person wearing red beat the person wearing blue, giving:
   # Name   Wore  Colour
   1 Gary   2     red
   2 Larry  3     green
   3 Barry  1     yellow
   4 Harry  4     blue

Workings

Hint
Who finished first? Start with Clue 2, and then Clue 4.

Answer
Zebra Wings         (ZW)
 Frog Flippers      (FF)
  Orange Berry      (OB)
   Apple Pie        (AP)
    Kipper Slippers (KS)
     CD Player      (CP)
      Top Hat       (TH)
       Windy Hill   (WH)
        Minty Mouth (MM)
         Fizzy Pop  (FP)

Reasoning
If we number the clues, write each name using two letters, and rewrite the clues so that those who finished ahead are written first:

ZW beat OB. ZW beat OB, FF and AP. MM, OB and CP, all beat FP. FF beat WH, CP and OB. CP, KS and AP, all beat TH. CP beat TH and FP. ZW and OB both beat AP. AP and FF both beat KS. FF beat FP, MM and CP. FF, KS and AP, all beat CP. TH beat FP and WH. WH and OB both beat MM. AP and CP both beat WH.
By (2): ZW FF
By (4): ZW FF OB
By (7): ZW FF OB AP
By (8): ZW FF OB AP KS
By (10): ZW FF OB AP KS CP
By (5): ZW FF OB AP KS CP TH
By (11): ZW FF OB AP KS CP TH WH
By (12): ZW FF OB AP KS CP TH WH MM
By (3): ZW FF OB AP KS CP TH WH MM FP

Workings

Hint
Look at the tops of the towers.

Answer
Add the two lines to the second tower from the left to complete the 'X' in the inverted letter sequence U, V, W, X, Y forming the towers' roofs.

Workings

Hint
Start by counting the letters you're already given.

Answers
This sentence contains one X. Slightly trickier, this sentence contains four R's. Even trickier, this sentence contains precisely ten E's. This sentence has exactly thirty-nine letters. This sentence, hopefully, contains seventy-five letters, one hyphen, five commas, and four Y's. To finish, if this sentence had a T removed, it would contain sixty-two letters!