Pizza Party On Algebra Avenue

15 Points Per Correct Answer - No time limit  

1. First of all we have to find my friends Alice and Bill, who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. I can't remember where Alice and Bill live, but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of "12".) I also remember that the sum of their two house numbers is a perfect square. The difference between their two house numbers is also a perfect square. Alice lives in the house with the smaller house number. What is the number of Bill's house? Answer: (Just type in the two-digit number.)

2. Now we have to find my friends Charlie and Debra, who live in two different houses on Algebra Avenue. I can't remember their house numbers either, but I remember that they are the reverse of each other. The sum of their house numbers is a perfect square, and the difference between their house numbers is a perfect cube. Charlie lives in the house with the smaller house number. What is the number of Debra's house? Answer: (Just type in the two-digit number.)

3. Now that we've found everybody, we need to go back to my house to get some money. I keep it in a rectangular box. Unfortunately, I own a lot of rectangular boxes, and I can't remember which one I put my money in. I remember that the three dimensions of the box (height, width, and length) are all whole numbers of inches, that they are all different, and that none of the dimensions is a prime number. I also remember that the volume of the box in cubic inches is the same as the total surface area of all six sides of the box in square inches. What is this volume or surface area? Answer: (Just type in the number, no units.)

4. Now we've found the right box, but I forgot it has a lock on it. It's one of those locks where you have to punch in a certain number to open it. I can't remember what the number is, but I remember that it's a four-digit number. I also remember that the sum of all four digits is equal to the product of all four digits, and that the four-digit number is evenly divisible by this sum or product. By the way, I also remember that the four-digit number is not "0000". What is it? Answer: (Just type in the four-digit number.)

5. Now I have my money. I'll let you choose whatever toppings you want on your pizza if you can figure out how much I have. I have a certain number of one-dollar bills (more than zero) and a certain number of ten-dollar bills (more than zero.) The number of one-dollar bills multiplied by the number of ten-dollar bills is equal to the total amount of money I have in dollars. The number of ten-dollar bills is not a prime. How much money do I have? Answer: (Just type in the number, no dollar sign.)