PLEASE I REALLY NEED YOUR HELP These problems are from my up

PLEASE! I REALLY NEED YOUR HELP! These problems are from my upper-division math class:

1. We may write all the digits from 1 to 9 in a row in any order we like, and then we write plus signs between some digits (as many plus signs as we like). For example, we could write 7 + 35 + 19 + 4 + 286. Finally, we evaluate the obtained expression. Prove that there is no way to get the value of 100. Or 101. Or 102. Or 103... What is the smallest three-digit number that can be obtained in this game?

3. Prove that an 8 x 8 board cannot be covered by 15 T-tetrominoes and one square tetromino.

Solution

3.Do the following: color every cell on an odd row in white and color every cell on an even row in black. Suppose that the board can be covered with 15 L-shaped tetrominos and one square-shaped tetromino. Notice now that since your L-shaped tetrominos will always cover an odd number of white cells and your square-shaped tetromino will alway cover an even number of white cells the total number of covered white cells will be always be odd. But this is not possible since the total number of white cells is 32 which is an even number. Contradiction.