Here are three simple math problems. They are intended to be solved analytically, with number theory, without using a computer or a calculator. But I cheated. All three problems come from the YouTube channel Mind Your Decisions, where you will find lots of similar problems.

  1. Solve for x and y where both are integers: 615 + x2 = 2y
  2. Find a three-digit number abc = 100a + 10b + c with none of the digits 0 such that abc = a! + b! + c!
  3. Find a three-digit number pie = 100p + 10i + e with none of the digits 0 such that √pi + e = √ pie

Your task is to solve the three problems; you can write programs to solve them, if you wish, but it is fun to solve them by hand. When you are finished, you are welcome to or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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