Pick any number and add 1 to it. Find the sum of the new number and the original number. Add 9 to the sum. Divide the new sum by 2 and subtract the original number from the quotient.

(a) What is the final number?

(b) Arbitrarily select some different numbers and repeat the process. Record the results.

(c) Can you make a conjecture about the final number?

(d) Prove, using deductive reasoning, the conjecture you made in part (c).