Medium Puzzles 

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.

Workings

Hint
The first letters of the words are: P, O, B, C, U, R, D, V, D, D, N, S, B, T, D.

Answers
---cil = pencil ---hid = orchid ---nze = bronze ---ese = cheese ---lug = unplug ---som = ransom ---uxe = deluxe ---uum = vacuum ---arm = disarm ---amo = dynamo ---rby = nearby ---ink = shrink ---sai = bonsai ---too = tattoo ---fen = deafen