Logic Deduction from Clues (Grades 6–7)
A deduction puzzle gives clues and asks you to find the one answer that fits all of them.
Understanding deduction from clues
The method: start with the numbers (or options) that satisfy the first clue, then eliminate any that fail the next, repeating until one remains. Each clue narrows the field.
Seeing it in action
Worked example
"I'm a number from 1–10. I'm even. I'm greater than 5. I'm less than 8." Who am I?
Even, 1–10: 2, 4, 6, 8, 10. Greater than 5: 6, 8, 10. Less than 8: only 6 is left → 6.
Even numbers 2 to 10; greater than 5 leaves 6, 8 and 10; less than 8 leaves 6.
A common mistake, and the fix
Answering before every clue is used.
After “even” and “greater than 5”, 6 looks right, but 8 and 10 fit too; only the last clue, “less than 8”, leaves 6 alone. If two numbers still fit after the last clue, the puzzle needs another clue, not a guess.
Try a few
"Odd, 1–10, greater than 6, not 9."
odd: 7,9; >6: 7,9; not 9: 7.
"Even, less than 6, greater than 2."
"Multiple of 3, 1–10, odd, less than 8."
3,6,9 → odd: 3,9 → <8: 3.
Two-Ring Outpost
A calm two-circle Venn diagram game for sorting sets and practicing AND/OR logic.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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