Grade 7 Math Puzzle 1: Undo a repeated routine in reverse

A free grade 7 math puzzle that teaches Undo a repeated routine in reverse. Try it first — the hint and the full solution open when you are ready.

Problem 1 · Undo a repeated routine in reverse · 3 points

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A machine doubles a two-digit number, adds 7, then swaps the digits of the result. It runs this routine twice and displays 53. What number went in first?

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What must the screen have shown just before the very last digit swap?
Work backward through the last round to find the number between the two rounds. Then work backward through the first round.

Show the answer and solution

Answer: C — 17

Working backward, swap 53 to get 35, subtract 7 to get 28, and halve to get 14. But 14 was the input to the second round, not the first. Swap 14 to get 41, subtract 7 to get 34, and halve to get 17. Checking forward: 17 → 34 → 41 → 14 → 28 → 35 → 53.

Grade 7 puzzle 1: Undo a repeated routine in reverse

Problem 1 · Undo a repeated routine in reverse · 3 points