What word does this rebus represent?

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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 to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

A cricket has 6 legs, a squirrel has 4 legs and a spider has 8 legs.

In a local zoo, it was found that the total number of legs is 612. Also, there are equal number of each of the above animals/insects.

Can you find out how many animals are there in the zoo?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

A container contains 100 eggs. They can be either fresh or rotten. What is sure is the fact that there is at least one fresh egg in that container.

If you are asked to pick two eggs randomly from the container, at least one of them will be rotten.

Can you calculate how many eggs in that container are fresh?

A Scientist was fifty years old in the year 2000 but he was forty years old in the year 2010. How can this be possible?

PS: It has a logical answer.

A Club organizes a Running Race, and John, Jacob, Minda, and Tony participated.

The results are as follows

John beats Jacob
Minda beats Toni
Toni beats John

Who came first in the race?

There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?