A classic math teacher trick has students perform a series of arithmetic operations on an “unknown” number, and at the end, the teacher guesses the number the students are thinking of. The trick is...

A classic math teacher trick has students perform a series of arithmetic operations on an “unknown” number, and at the end, the teacher guesses the number the students are thinking of. The trick is that the final number is always a constant the teacher knows in advance. One such example is doubling a number, adding 10, halving it, and subtracting the original number. Using a series of small helper functions chained together, map this process across all numbers between 1 and 100. How does the teacher always know what number you’re thinking of?