How much does the answer depend on what you pick? Four questions, four different replies — and the last one is not a number.
The answer key prints on a separate page.
Section 1 hands over a completely free choice at every step and the answer is the same anyway: rub out any two numbers, write their sum minus one, repeat. Every child in the room chooses differently and every one of them finishes on the same number, because it was fixed before the first move. Section 2 goes the other way — two purchases, three prices, and questions the facts genuinely do not decide, where the honest answer is CANNOT TELL and the proof is two price lists that both fit and disagree. Section 3 puts a real opponent across the table who is trying to win, and the strategy still holds against every move they make. Section 4 decides nothing at all: the child writes the question, and every valid one is on the key.
The order is what makes each section land. A child who has just watched their own choices fail to matter meets a page where they matter completely, then a game where the OTHER person's choices cannot help them, and finally a page with nothing yet to choose between at all. Asked separately these are four puzzles; asked in this order they are one question about how much a mathematical answer is ever up to you.
