Random Puzzles 

Workings

Hint
How old could Glen be?

Answer
Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

Reasoning
The possible ages are: 15, 16, 18, 19.

Breaking the clues down, and numbering them:
Frankie beat Glen in chess. Dale came third (chess). The 16-year-old won (chess). Frankie came second in croquet. The 15-year-old won (croquet). Dale beat the 18-year-old (croquet). The 19-year-old came third (croquet). Emery is 3 years younger than Glen. The person who came last in chess came third in croquet. Only one person got the same position in both games.
By (4), Frankie came 2^nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3^rd in chess.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen

By (8), Emery is 15 or 16, and Glen is 18 or 19.

By (9), the person who came 4^th in chess, came 3^rd in croquet, and by (7), they are 19. This can't be Dale (3^rd in chess), or Frankie (2^nd in croquet), or Emery (aged 15 or 16), so it must be Glen.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen    19     4      3

By (6), Dale can't have been 4^th in croquet, so must be 1^st. Leaving Emery in 4^th.
Name    Age    Chess  Croquet
Dale           3      1
Emery                 4
Frankie               2
Glen    19     4      3

By (10), only one person got the same position in both games, this can't be Emery 4^th in both (as Glen is already 4^th in chess), so must be Frank, 2^nd in both. Leaving Emery 1^st in chess.
Name    Age    Chess  Croquet
Dale           3      1
Emery          1      4
Frankie        2      2
Glen    19     4      3

By (3) and (5) we know the ages of the winners in each competition, and Frankie is therefore 18.
Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

Workings

Hint
The first letters of the words are: R, S, D, E, C, W, Z, A, M, D.

Answers
Rabbit Squirrel Donkey Elephant Cat Weasel Zebra Aardvark Mouse Dog

Workings

Hint
Think of the pages from 1-9, and then 10-99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.

For pages 10-99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, …, 143

We also have the ten pages that start with 30:

   30, 31, 32, …, 39

Plus the ten pages that start with 130:

   130, 131, 132, …, 139

For a total of 15 + 10 + 10 = 35 number 3's.

Workings

Hint
Look at Clue 3 first, and then Clue 5.

Answer
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor        Arnold
————————————————————————
#2  Jamie         Pat
    Bowler        Watson
————————————————————————
#3  Sam           Billie
    Arnold        Taylor
————————————————————————
#4  Pat           Jamie
    Watson        Bowler

Reasoning
The four names were: Billie, Jamie, Pat, Sam
The four contestants were: Arnold, Bowler, Taylor, Watson.

By (3), Billie Taylor came third in the second race, and Pat came last in the first race, giving:
    Race1         Race2
————————————————————————
#1

————————————————————————
#2

————————————————————————
#3                Billie
                  Taylor
————————————————————————
#4  Pat
 

By (5), in the first race Billie beat Jamie, and Jamie beat Sam, giving:
    Race1         Race2
————————————————————————
#1  Billie
    Taylor
————————————————————————
#2  Jamie

————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat
 

By (2), Sam beat the runner with the surname Watson in the first race, which means that Pat's surname is Watson, giving:
    Race1         Race2
————————————————————————
#1  Billie
    Taylor
————————————————————————
#2  Jamie

————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat
    Watson

By (1), Pat can't have also finished in last place in race 2, and by (2), Sam beat the Pat Watson, so Pat must have finished in second place in race 2. And Sam came first, therefore Jamie came last, giving:
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor
————————————————————————
#2  Jamie         Pat
                  Watson
————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat           Jamie
    Watson

By (4), in the second race the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last, so we know Sam and Jamie's surnames, and we can complete the grid:
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor        Arnold
————————————————————————
#2  Jamie         Pat
    Bowler        Watson
————————————————————————
#3  Sam           Billie
    Arnold        Taylor
————————————————————————
#4  Pat           Jamie
    Watson        Bowler