← Curifold Puzzle School · 7 minutes ·
A fictional number machine starts with a whole number from 1 to 10. It doubles the number, then adds 3. The display shows 17. Find the starting number by undoing the steps.
- Start: integer 1–10
- Double, then add 3
- Display: 17
The idea
Undo the last operation first. Subtracting 3 reverses adding 3, and dividing by 2 reverses doubling. Record the intermediate values, then run your candidate through the original instructions. This catches reversed-order mistakes. Some processes lose information, such as rounding; not every process has a unique reverse. This machine does within its stated range.
Try it yourself
The clues
- The starting number is a whole number from 1 to 10.
- Double it, then add 3.
- The result is 17.
| Stage | Action | Value |
|---|---|---|
| Display | Known output | 17 |
| Undo addition | Subtract 3 | Your answer |
| Undo doubling | Divide by 2 | Your answer |
Hint 1
What was the value just before the machine added 3?
Hint 2
What number doubles to 14?
What is the starting number?
17 minus 3 is 14, and half of 14 is 7. The forward check gives 17.
10 would produce 23, so it does not satisfy the output clue.
This divides too early and also breaks the whole-number rule.
Read all responses and explanations
7
17 minus 3 is 14, and half of 14 is 7. The forward check gives 17.
10
10 would produce 23, so it does not satisfy the output clue.
8.5
This divides too early and also breaks the whole-number rule.
Which reverse sequence is valid?
The original last operation must be undone first, not last.
This reverses both operations in the correct order.
Adding 3 again does not undo the original addition.
Read all responses and explanations
Divide by 2, subtract 3.
The original last operation must be undone first, not last.
Subtract 3, divide by 2.
This reverses both operations in the correct order.
Add 3, divide by 2.
Adding 3 again does not undo the original addition.
Reveal the complete solution
17 − 3 = 14; 14 ÷ 2 = 7. Only 7 among the ten allowed inputs produces 17. Forward check: 7 × 2 + 3 = 17.
Make it your own
Make another machine: add 4, then triple. Starting with 2 produces 18. Explain why undoing it requires division by 3 before subtraction of 4. Check your reasoning by running the answer forwards.
Your takeaway
- Record the original operations
- Undo the last operation first
- Write each intermediate value
- Check the allowed input range
- Run my answer forwards
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Original fictional educational practice, separate from the puzzles sold in the books. Use the stated rules; there is no speed target or score.
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Original educational content by Andrew Stinson Books, developed with AI assistance. Our editorial approach.