Logic Riddles

Question: You have an 8 by 8 chess board that has two corner squares diagonal from each other removed. Is there any way to place 31 dominoes of size 2x1 to cover the remaining 62 spaces?

Question: A king is on a cross-sea voyage and as soon as they get off of their boats he spots the most beautiful elephant he has ever seen. He decides to take it home, but first, he wants to know its weight.

The largest scale they brought only goes up to 50 pounds. The king demands that his smartest scholar must come up with a solution or pay the consequences. After several days he finally comes up with an answer.

Question: What is the best way to stop a dog from barking in, and digging up the front yard?

Question: When is 1500 plus 20 and 1600 minus 40 the same thing?

Question: A school's computer system was recently hacked and the school has narrowed the pool of possible hackers to 5 people that were in the computer lab: Tyler, Justin, Chandler, Paige, and Shelley. Each of them gave three statements, two of which are true and one false.

Tyler
1. I didn't do it!
2. I've never hacked in my life.
3. Paige did it.
Justin
1. I didn't do it!
2. The attack was done from within the network.
3. I don't like Shelley.
Chandler
1. I didn't do it!
2. I've never seen Shelley in my life.
3. Paige did it.
Paige
1. I didn't do it!
2. Shelley did it.
3. Tyler was lying when he said I did it.
Shelley
1. I didn't do it!
2. Justin did it.
3. Chandler and I used to be friends.

Who hacked the system?