These problems are my attempt to give high school students, like you, a glimpse into "real mathematics" by creating a math puzzle which will challenge you to think in ways that you have never thought before. Typically, in your high school math classes, you are given a problem to solve and a fixed step-by-step procedure for solving that type of problem — follow the steps, and you are certain to get an answer. However, "real mathematics" is not like that. When mathematicians work on problems, they often start off with no idea about how to solve the problem. There are lots of math questions that no one yet knows how to solve. I invite you to stretch your mind and take my mathematics challenge. I look forward to see what you come up with — Joseph DiMuro, Assistant Professor for the Department of Math and Computer Science.
Picture this: you're on a strange game show. The host shows you five boxes, and tells you that each contains a different amount of money: $1000, $2000, $3000, $4000, or $5000. Your task is to put the boxes in order, from smallest amount to largest amount. If you succeed, you win the entire $15000 in the boxes.
You're not allowed to look inside the boxes, or pick them up and shake them, or anything like that. Instead, to figure out how much money is in each box, you can ask the host a series of questions. You can point to two of the boxes, and ask the host which of those two boxes has more money (the host will answer truthfully). You may ask 7 such questions. After that, you have just one chance to put the boxes in the right order. You win the $15000 if you are right; otherwise, you win nothing.
What strategy would you follow to maximize your chances of winning the grand prize? And what is the probability of winning if you follow that strategy?
Joseph DiMuro (email@example.com) by December 16, 2016.
I will review your submission and whether you are correct or incorrect, I will be in touch with you to provide personal feedback, guidance, and background information regarding the problem.