Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

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
=========

If 21x = 79x, what is the value of x?

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

Can you replace the question mark with the correct letter?

6 + 6 + 6 = N
7 + 7 + 7 = E
8 + 8 + 8 = R
0 + 0 + 0 = ?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

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?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you can't go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfil the condition given?