Random Puzzles 

Workings

Hint
The answers are related to time.

Answer
60.

The numbers represent 100 years in a century, 365 days in a year, 24 hours in a day, 60 minutes in an hour and 60 seconds in an minute.

Workings

Hint
Does ONE work, does TWO work? How many E's are there already?

Answer
Twelve.

"Cleverly, there are exactly twelve E's in this sentence."

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
A very tricky puzzle involving prime numbers.

Answer
101.

These are prime numbers, which, when reversed, are also prime.