# find the order of fruits

There are five fruits (Apple, Banana, Pineapple, Orange and Watermelon) that should be ordered in their places. But we do not have enough containers for them: there are only two bowls and two baskets. So one of the fruits will remain without container.

We also know that both baskets are larger than either bowl.

1. The watermelon is larger than all the other fruits.
2. The bowls are too small for the pineapple to fit in.
3. The two bowls are not neighbors.
4. The apple is the smallest fruit, and it is in a container at the center.
5. The banana is between two baskets.
6. The largest fruit and the smallest fruit are not neighbors.
7. The fruit without container has two neighbor fruits in containers.

Which fruit will remain without container? Also find the order and place of the fruits and containers with following clues: (note that the orientation does not matter, left to right or right to left)

Source: myself

• For 5, do you use "between" to mean that the banana has two neighbours that are both baskets, or that there is a basket somewhere to the left and somewhere to the right? It doesn't change the solution, but it makes 3 a required piece of information. – LeppyR64 Sep 15 '14 at 15:03
• @JasonLepack It meant to be two basket neighbors. but you are right, it will be interesting to be somewhere to the right and somewhere two the left. +1 – Rafe Sep 15 '14 at 15:16

1. The watermelon is larger than all the other fruits.
2. The bowls are too small for the pineapple to fit in.
3. The two bowls are not neighbors.
4. The apple is the smallest fruit, and it is in a container at the center.
5. The banana is between two baskets.
6. The largest fruit and the smallest fruit are not neighbors.
7. The fruit without container has two neighbor fruits in containers.

I'll use A, B, P, O, and W for the fruits; K for basket, L for bowl, and N for neither.

Directly from 4:

_ _ A _ _
_ _ _ _ _


1 + 4 + 6 -> watermelon is on one side (we'll pick one and call it left).

W _ A _ _
_ _ _ _ _


From 7 we know it's in a container (since it doesn't have two neighbors), and from 1 + 2 we know that has to be a basket.

W _ A _ _
K _ _ _ _


From 5 we can then deduce both that the banana is second from the left and the apple is in a basket.

W B A _ _
K _ K _ _


From 3 we can see the banana is in a bowl, and from 7 we can tell the other bowl has to be on the far right, leaving the fruit without a container next to it.

W B A _ _
K L K N L


From 2 we know the pineapple can't be in the bowl on the right, so that leaves the containerless spot for it, and the bowl for the orange:

W B A P O
K L K N L


So, in English, the order is:

2. Banana in a bowl
4. Pineapple without a container
5. Orange in a bowl

Actually, 3. is an unnecessary condition. From

W B A _ _
K _ K _ _


you can continue:
From 7. the last position is a bowl.
From 2. the pineapple is not in the bowl, it must be the orange.

W B A _ O
K _ K _ L


The pineapple is the last fruit and it cannot be in a bowl

W B A P O
K L K N L

• thats right! +1 – Rafe Sep 14 '14 at 13:04