Which word does the below Plexor means ?

You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I am double, I am single,
I am black blue and grey,
I am read from both ends,
And the same either way.

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
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I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

Rearrange the letters in "new door" to make one word.

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)