Christmas Special 2014 - Deer Oh Deer (Solution)

The answer is 94. Clue 1 states that Prancer took twice as many presents as Cupid. Thus Prancer = 2 Cupid. However, Clue 4 states that Comet = Cupid - 2 and Comet = Prancer - 33. Thus Cupid - 2 = 2 Cupid - 33. Solving for Cupid, we have Cupid = 31, Comet = 29, and Prancer = 62.

Clue 1 also states that Dasher = 2 Vixen. Clue 3 states that Dancer = Vixen + 5 and Donner = Dancer + 1. Thus Donner = Vixen + 6. However, Clue 5 states that Donner = Dasher - 27. Thus Vixen + 6 = 2 Vixen - 27. Solving for Vixen, we have Vixen = 33, Dancer = 38, Donner = 39, and Dasher = 66.

Now we can use Clue 6, which says that Donner = (Blitzen + Comet) / 2. This Blitzen = 2 Donner - Comet = 2 * 39 - 29 = 49. There are 9 reindeer so the average is one-ninth of the total. Thus Blitzen = Total / 9 and Total = 441. Rudolph can now be worked out as 441 - 31 - 29 - 62 - 33 - 38 - 39 - 66 - 49 = 94. Thus Rudolph took 94 presents.

At first sight, nothing is told about Rudolph in any of the clues. This leads many to think that the puzzle is unsolvable. People could resort to subtracting all other numbers from the total to get Rudolph until they realise that the total is not given. However, Clue 2 references the average. Multiplying by the number of reindeer can give the total. This is required to work out the number of presents Rudolph took.

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