Annals of Xanadu – Problem 1

In the land of Xanadu, all problems have a perfect solution! Oh that we all could live in Xanadu!

On this day, the wise ruler of Xanadu reconvenes their court. A trade treaty is in question. The treaty will involve a shipment of goods to the neighbouring nation once every month. Each shipment will consist of exactly five goods – two energy goods, and three domestic goods. The energy goods are petrol and solar panels. The domestic goods are textiles, wheat, and detergent. Each shipment must be structured as follows:

• There are exactly two ships provided for each shipment, one launched after the other. The first ship is large enough to carry three goods, and the second ship is large enough to carry two.
• Within each ship, goods are ordered by bulk size, from largest to smallest.
• Each ship contains at least one domestic good.
• The solar panels are always the largest of the five goods.
• The detergent is always the smallest of the five goods.
• There is always more petrol than wheat.

1. Five ministers approach the ruler of Xanadu with proposals on how to arrange the goods aboard the ships. Which one of their proposals would be a valid arrangement of goods aboard the ships?

A. First ship: petrol, solar panels, textiles
     Second ship: detergent, wheat

B. First ship: solar panels, petrol, textiles
     Second ship: wheat, detergent

C. First ship: solar panels, textiles
     Second ship: petrol, wheat, detergent

D. First ship: solar panels, wheat, petrol
     Second ship: detergent, textiles

E. First ship: detergent, wheat, textiles
    Second ship: solar panels, petrol

2. As the ruler decided on the correct choice, an attendant entered the chamber and announced a new arrangement for the ships. The textiles would have to be the last good on the first ship. The ministers got confused with this new information and asked the ruler a question. Which one of the following must be true?

A. The solar panels are the first good on the first ship.

B. The petrol is the second good on the first ship.

C. The wheat is the second good on the first ship.

D. The solar panels are the first good on the second ship.

E. The detergent is the last good on the second ship.

3. As the ruler decided the correct choice, an attendant entered the chamber and announced a new arrangement for the ships. The solar panels would have to be the first good on the second ship. With this new information, the ruler puzzled out exactly how many of the goods are there any one of which could be the first good in the first ship.

A. one

B. two

C. three

D. four

E. five

4. Once the ruler figured out the correct answer, the attendant relaying the information said that things have changed, and only the original rules now applied. To avoid future confusion, the ruler determined to decide what about the arrangement cannot be true.

A. The petrol is the first good on the first ship.

B. The solar panels are the first good on the first ship.

C. The solar panels are the first good on the second ship.

D. The wheat is the first good on the first ship.

E. The wheat is the last good on the second ship.

5. While at it, the ruler determined that the order of goods would be fully determined if one of the following was true:

A. The petrol is the last good on the first ship.

B. The solar panels are the first goods on the first ship.

C. The solar panels are the first goods on the second ship.

D. The textiles are the last goods on the second ship.

E. The wheat is the last good on the first ship.

6. Then the attendant returned and announced that the textiles would have to be the first good on the first ship. The ruler then determined which one of the following options could be true:

A. The petrol would be the first good on the second ship.

B. The solar panels would be the second good on the first ship.

C. The wheat would be the second good on the first ship.

D. The wheat would be the first good on the second ship

E. The wheat would be the last good on the second ship.

Thanks to the wise guidance of the ruler, the ships left the Xanadese dock and built a healthy trade relationship with their neighbour.

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Legend

1. B
2. E
3. B
4. D
5. A
6. E