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?

Mrs. Stotch is a fifth grade teacher. One of her students took her apple. Mrs. Stotch has narrowed the suspects down to Billy, Paige, and Tyler. Each of these students give these statements:

Billy: I didn’t do it.
Paige: I didn’t do it.
Tyler: Paige did it!

Mrs. Stotch knows that only one of the kids is telling the truth. Which one is telling the truth and who took the apple?

You have two buckets: one with only white marbles and one with only black marbles. The two buckets have the same number of marbles.

How can you rearrange the marbles to maximize your chances of grabbing a white marble from each?