Medium 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 2nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3rd 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 4th in chess, came 3rd in croquet, and by (7), they are 19. This can't be Dale (3rd in chess), or Frankie (2nd 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 4th in croquet, so must be 1st. Leaving Emery in 4th.
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 4th in both (as Glen is already 4th in chess), so must be Frank, 2nd in both. Leaving Emery 1st 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
Find anagrams of the words in this order: PLEASE, TRANCE, LISTEN, WARNED, VEINED, BRUISE.

Answers
ANSWER.

Reasoning
The initial letters are RWASEN, which is an anagram of ANSWER.
bruise becomes rubies warned becomes wander please becomes asleep listen becomes silent veined becomes envied trance becomes nectar

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

Workings

Hint
Going down and across the floor isn't the only route.

Answer
40 feet.

Explanation Diagram
If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.



We can use Pythagoras' theorem (a² + b² = c²) to calculate the distances:
   distance² = horizontal² + vertical²
   distance = √(horizontal² + vertical²)

Route #1
   distance = 1 + 30 + 11 = 42 feet.

Route #2
   horizontal = 6 + 30 + 6 = 42 feet.
   vertical = 10 feet.
   distance = √(42² + 10²) ≈ 43.174 feet.

Route #3
   horizontal = 1 + 30 + 6 = 37 feet.
   vertical = 6 + 11 = 17 feet.
   distance = √(37² + 17²) ≈ 43.178 feet.

Route #4
   horizontal = 1 + 30 + 1 = 32 feet.
   vertical = 6 + 12 + 6 = 24 feet.
   distance = √(32² + 24²) = 40 feet.