Can you decipher the following common phrase?

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

I am dry when I go inside, but wet when I am pulled outside.
The longer I am inside, the stronger I get
When I am completely out, I am wet and I literally sag
Who am I?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

Why is the Hole below a Lock?

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?

The centre of the third figure is empty. What digit should fit inside?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?