1. I'm going to roll two dice. We both have to pick a number, and whoever's number is closest to the dice roll wins. Do you prefer to pick first or second? 2. You have the numbers between 1 and 30. What is the largest sum you can make by picking out numbers but only using each prime factor once? (For example, if you pick 6, you can't pick any other number with a factor of 2 or 3.) 3. You have a safe with a six-digit code and a light. You can input a code: if you have between 0 and 3 of the 6 digits correct, the light will turn red; if you have 4 or 5 correct, it will turn yellow; if you have all 6 correct, it will open. There is $10,000 inside. You can guess the code as many times as you want, but you have to pay for each guess. How much would you be willing to pay per guess?