What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?

A mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

What is the word or phrase?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?