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Thursday, December 03, 2015

Stocking Fillers

Information you need to know:

In a quiet house on Christmas Eve, a mother and father are busily beavering away stuffing stockings for their seven daughters and attaching them in a row along their (thankfully large) mantelpiece. Can you identify the intended recipient of each stocking, the edible item lovingly stowed away in it and the position in which it has been pinned to the mantelpiece? (The positions are numbered 1 to 7 from left to right from the perspective of someone facing the mantelpiece.)

The seven daughters are named Bronwyn, Cammy, Darcy, Donna, Prudence, Ruby and Victoria.
The seven stocking fillers used are apples, bananas, biscuits, chocolates, nuts, oranges and toffees.

1. Victoria's stocking is positioned between those belonging to Darcy and Donna, neither of which are at the end of the row in positions 1 or 7. The bananas and the biscuits are not in any of the three aforementioned stockings.
2. In ascending numerical order, three neighbouring stockings contain nuts, chocolates and apples respectively.
3. Oranges are Cammy's favourite fruit, so were the first thing that went in her stocking.
4. The position of Prudence's stocking is numbered one higher than Darcy's, but has a lower number than Bronwyn's.
5. The bananas are sitting in the stocking at position number 6; Ruby's stocking is hanging in position number 3.
6. Donna hates toffee, so unsurprisingly her parents didn't put any in her Christmas stocking.

And now the questions begin:

1. Who does the stocking in position number 1 belong to?

2. Victoria's stocking is hanging in which position?

3. What position number is Darcy's stocking hanging in?

4. What edible stocking filler is in Prudence's stocking?

5. Bronwyn's stocking is located on one end of the mantelpiece (i.e. in position 1 or 7). True or false?

6. What is in Donna's stocking?

7. One of the sisters found a stash of chocolates in a stocking hanging in which numbered position?

8. Who ended up with the apples?

9. What edible treat did Darcy receive?

10. What was placed in the stocking at position 7?

And now the answers:
1. The correct answer was Cammy
Clue 1 rules out Darcy, Donna and Victoria. From clue 4 it also can't be Prudence or Bronwyn as their stockings must both be in a position with a higher number than Darcy's. Clue 5 states that Ruby's stocking is at position number 3, which just leaves Cammy as the owner of stocking at position 1.

2. The correct answer was 4
From clue 1 we know that Victoria's stocking can't be in position 1 or 7 and is located between those belonging to Darcy and Donna (which also can't be at positions 1 or 7) - therefore it can't be at position number 2 or 6 either. Clue 5 rules out position 3 (as that is Ruby's), leaving a choice between 4 or 5. If it was at position 5 then either Darcy's or Donna's would have to be at position 6 - but that is impossible because neither of those girls received bananas (clue 1) and clue 5 confirms the presence of bananas in that stocking. Therefore Victoria's must be at position number 4.

3. The correct answer was 5
We can use clue 1 to rule out positions 1 and 7 straight away; clue 5 rules out position 3 and, in conjunction with clue 1, position 6 (because of the bananas). The answer to question 2 rules out position 4 (Victoria's). That leaves positions 2 and 5. If Darcy's was at position 2, then Prudence's would have to be at position 3 (clue 4), but that is impossible because that stocking belongs to Ruby (clue 5). Therefore Darcy's is at position number 5.

4. The correct answer was bananas
Prudence's stocking is at a position numbered one higher than Darcy's (clue 4), which is at position 5 (question 3). Therefore it must be at position 6 and clue 5 tells us that that stocking contains bananas.

5. The correct answer was 't'
From clue 4, Bronwyn's stocking is at a position with a higher number than Prudence's. Question 4 and clue 5 tell us that Prudence's is the one with bananas in position 6, meaning that Bronwyn's must be at position 7. Therefore it is true that it is hanging on one end of the mantelpiece - the right hand side to be precise!

5. The correct answer was nuts
Donna does not have bananas, biscuits, oranges or toffees in her stocking (clues 1, 3 and 6). That leaves nuts, chocolates or apples, which appear in neighbouring stockings, with nuts being in the one at the lowest numbered position of the three (clue 2). These stockings can only be at positions 2, 3 and 4 or 3, 4 and 5 respectively, as we already know that the stocking at position 1 contains the oranges (question 1 and clue 3) and the one at position 6 contains the bananas (clue 5). We also know that Donna's stocking must be hanging in position 2 as it must be to the left of Victoria's (in position 4) - since Darcy's is to the right (questions 2 and 3 and clue 1) - but can't be at position 1 (from clue 1) or position 3 (from clue 5). Putting these two facts together leaves the nuts as the only possible filler for Donna's stocking.

7. The correct answer was 3
From question 6 and the workings required to obtain the answer we know that the nuts are in Donna's stocking in position 2. From clue 2 we know that the chocolates were placed in the stocking at the position numbered one higher than the stocking containing the nuts. Therefore the chocolates are in the stocking at position 3.

8. The correct answer was Victoria
From clue 2 we know that the apples are in the stocking at the position numbered one higher than that where the stocking containing the chocolates is hanging. Since we know that the chocolates are in the stocking at position 3 (question 7) the apples must be at position 4, which belongs to Victoria (question 2).

9. The correct answer was toffees
Darcy did not receive bananas or biscuits (clue 1), oranges (clue 3), nuts (question 6) or apples (question 8). Also, the chocolates are in the stocking at position 3 (question 7) and Darcy received the stocking hanging at position 5. Therefore Darcy received the toffees.

10. The correct answer was biscuits
It can't be the bananas, which are in the stocking at position 6 (clue 5). We can also rule out the chocolates that are at position 3 (question 7) and therefore the nuts at position 2 and the apples at position 4 (clue 2). The oranges were given to Cammy (clue 3) who received the stocking at position 1 (question 1) and the toffees were left for Darcy in the stocking at position 5 (questions 3 and 9). That just leaves biscuits.

The full solution is as follows:

Stocking 1 - Cammy - Oranges
Stocking 2 - Donna - Nuts
Stocking 3 - Ruby - Chocolates
Stocking 4 - Victoria - Apples
Stocking 5 - Darcy - Toffees
Stocking 6 - Prudence - Bananas
Stocking 7 - Bronwyn - Biscuits

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