"I am a four-digit number. My digits add to 16. It is a multiple of 4. The thousands digit is 5 more than the ones digit." Nine thousand numbers fit the first line. One fits all of them.
Every clue is a relation — a sum, a difference, a multiple, a comparison — and not one of them names a digit. That is deliberate and it is what makes the puzzle a puzzle: a clue like "the thousands digit is 8" turns the sheet into four small questions wearing one sentence, and a child fills the number in left to right without ever holding two facts at once.
Why this sheet works
The clue sets are pruned until every clue is load-bearing: remove any single one and more than one number fits. So a child who ignores a clue cannot arrive, and a child who has used them all is finished — there is no spare hint to make the last step guessable.
1I am a four-digit number. The first two digits add to 6. Its four digits add up to 12. The thousands digit is 6 more than the ones digit.What number am I?Why
2I am a four-digit number. The first two digits add to 9. Its four digits add up to 20. The thousands digit is 7 more than the ones digit.What number am I?Why
Who am I?Up to 3 clues
Name: Date:
Use every clue. Show what each one rules out.
3I am a four-digit number. Its four digits multiply to 80. The tens digit is double the hundreds digit. The first two digits add to 9.What number am I?Why
4I am a four-digit number. The thousands digit is 4 more than the ones digit. Its four digits multiply to 378. The first two digits add to 16.What number am I?Why
Who am I? · Up to 3 cluesAnswer key
1. Start with all 9000 four-digit numbers. The first two digits add to 6 → 600 left; Its four digits add up to 12 → 42 left; The thousands digit is 6 more than the ones digit → 1 left. That one is 6060.2. Start with all 9000 four-digit numbers. The first two digits add to 9 → 900 left; Its four digits add up to 20 → 72 left; The thousands digit is 7 more than the ones digit → 1 left. That one is 9092.3. Start with all 9000 four-digit numbers. Its four digits multiply to 80 → 48 left; The tens digit is double the hundreds digit → 4 left; The first two digits add to 9 → 1 left. That one is 8125.4. Start with all 9000 four-digit numbers. The thousands digit is 4 more than the ones digit → 600 left; Its four digits multiply to 378 → 4 left; The first two digits add to 16 → 1 left. That one is 7923.
