If Larisa's aisles are separated by the maximum number of aisles that could separate her aisles, which one of the fol...

Victoria on September 25, 2020

Hi @kenken,

Happy to help!

There are a couple issues with the setup you've outlined above.

First, K must stock Aisle 2. Second, there is only one aisle in between the two aisles that M stocks and that aisle is stocked by K.

Therefore, if L stocks Aisle 9, the maximum number of aisles separating L's two aisles could be 5. However, if L stocks Aisle 1, then the maximum number of aisles separating L's two aisles could be six.

This means that L must stock Aisles 1 and 8 for there to be the maximum number of aisles separating her aisles.

L K _ _ _ _ _ L _
1 2 3 4 5 6 7 8 9

If M stocks Aisle 7, then K must stock Aisle 6 and M must also stock Aisle 5 because of Rule 5 which tells us that k stocks the only aisle between the two aisles M stocks.

L K _ _ M K M L _
1 2 3 4 5 6 7 8 9

Rule 7 tells us that O's aisle is numbered higher than either of K's aisles. This would mean that O must stock Aisle 9. However, Rule 7 also tells us that O's aisle is numbered lower than at least one of L's.

Therefore, M cannot stock Aisle 7 without breaking at least one rule and cannot be true.

On the other hand, if L is separated by 6 aisles, then it is entirely possible that J stocks Aisle 6.

L K M K M J O L J
1 2 3 4 5 6 7 8 9

Notice that this meets all of our conditions, including the condition imposed by the question stem i.e. that L's aisles are separated by the maximum number of aisles which can separate them.

1) O stocks exactly one aisle: Aisle 7.
2) K stocks Aisle 2.
3) M does not stock Aisle 1.
4) J does not stock consecutive aisles. J stocks Aisles 6 and 9.
5) K stocks the only aisle between the two aisles that M stocks: M stocks Aisles 3 and 5 and K stocks Aisle 4.
6) Exactly one of L's aisles is an end aisle: Aisle 1.
7) O stocks Aisle 7. This is higher than either of K's aisles (Aisles 2 and 4) and lower than one of L's aisles (Aisle 8).

Hope this helps! Please let us know if you have any further questions.

Dina on August 12, 2021

i have one additional question can you explain why L cannot be on both ends of the scenario. like
L K J M K M J/O O/J L
1 2 3 4 5 6 7 8 9

Thomas on October 27, 2023

I'm not an instructor but if you look at rule #6, it states that "EXACTLY ONE of L's aisles is an end aisle." That means if we had the L aisles at both ends it would violate the rule that exactly one of them is an end aisle because you would have both and it wouldn't be 'exactly one'