Medium Puzzles 

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

Workings

Hint
What colour did Billie wear?

Answer
# Name    Wore  Colour
1 Alex    4     Red
2 Emery   2     Green
3 Billie  1     Blue
4 Glen    3     Yellow

Reasoning
(Clue 1) Alex won and wore Red. (Clue 5) Glen wore Yellow. (Clue 3) Billie wasn't wearing number 2, and (Clue 6) number 2 wore Green, so must be Emery. Leaving Billie in Blue.
   # Name    Wore  Colour
   1 Alex          Red
   ? Glen          Yellow
   ? Emery   2     Green
   ? Billie        Blue

(Clue 2) Emery didn't come 3^rd, and Alex won, so (Clue 5) Emery can't have come last, so must have come 2^nd.
   # Name    Wore  Colour
   1 Alex          Red
   2 Emery   2     Green
   ? Glen          Yellow
   ? Billie        Blue

(Clue 3) Billie can't have been last, so came 3^rd and (Clue 2) wore 1, leaving Glen in last place.
   # Name    Wore  Colour
   1 Alex          Red
   2 Emery   2     Green
   3 Billie  1     Blue
   4 Glen          Yellow

(Clue 5) Emery beat the student wearing 3, so Glen must have worn 3. Leaving Alex wearing 4.
   # Name    Wore  Colour
   1 Alex    4     Red
   2 Emery   2     Green
   3 Billie  1     Blue
   4 Glen    3     Yellow

Workings

Hint
The first letter can only be B.

Answer
A badger.

Reasoning
My first is in bridge, but not in ridge = B

My second is in awake, and in mistake = A K E

My third is in danger, but not in ranger = D

My fourth is in strange, and in orange = R A N G E

My fifth is in spline, and in nine = I N E

My last is in river, and in diver = R I V E

Workings

Hint
Does the number of adults and children matter?

Answer
3,672.

Reasoning
The actual number of adults and children doesn't actually matter.

If all of the people were adults, then half of them (306) would be given 12 sweets:

  306 x 12 = 3672

If all of the people were children, then three quarters of them (459) would be given 8 sweets:

  459 x  8 = 3672

If there were 512 adults (so 256 would get 12 sweets = 3072) and 100 children (so 75 would get 8 sweets = 600):

  256 x 12 + 75 x 8 = 3672

We can change the numbers of adults and children, but it doesn't change the answer.

The reason for this lies in the fact that ¹/₂ adults x 12 sweets = ³/₄ children x 8 sweets (both are 6).