🕵️Logic Puzzles

Logic puzzles hand you no formulas, only clues. Their charm: the clues never seem like enough, yet the answer is unique — as long as you reason one clean step at a time.

What logic puzzles train

Two core muscles:

• Deduction: from facts that certainly hold, derive facts that necessarily hold;
• Elimination: cross out the impossible options one by one, and whatever survives — however surprising — must be it.

One classic puzzle exercises both muscles at once.

Cracking a classic: the three boxes

Three boxes carry the labels “apples”, “oranges” and “mixed”, and every label is wrong — each box contains something other than what its label says. You may reach into one box, draw out a single fruit, and then say what each box contains. Which box do you pick?

The trick: pick the one labeled “mixed”.

• The label is wrong, so it cannot hold a mix — it is all apples or all oranges, and one fruit settles which;
• You draw an apple: that box is the “apples” box;
• Now the box labeled “oranges”: it cannot hold oranges (the label lies) and apples are already taken, so it holds the mix;
• The box labeled “apples” is left holding the oranges.

One fruit, three cases closed — the "all wrong" condition turns every single fruit into three clues.

Truth-table thinking

A promise like “if P, then Q” is broken in exactly one situation — so lay out all four cases first; that is truth-table thinking. Mom says: “Finish your homework and you get ice cream.”

• Homework finished, ice cream given: promise kept;
• Homework finished, no ice cream: promise broken — the one forbidden case;
• Homework skipped, ice cream given: the promise never triggered, nothing broken;
• Homework skipped, no ice cream: likewise no promise broken.

So “no homework finished, therefore surely no ice cream” is bad reasoning: when P is false, Q may go either way. Plenty of arguments collapse for lack of these four rows.

Strategy: list it, cross it out

• When possibilities are few, write out the full list honestly;
• Use the clues to strike out the impossible one at a time;
• One survivor: that is your answer. Several survivors: go find the clue you have not used yet;
• Before handing in, plug the answer back into every clue and check.

Place 1–9 so every row, column and diagonal sums to 15

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Remaining

123456789

💡 Show a sample solution↺

The magic square is an elimination gym: every row, column and diagonal sums to 15. The four lines through the center each need their other two cells to form a pair summing to 10 — (1,9), (2,8), (3,7), (4,6) are exactly four pairs, and together they swallow all the other eight numbers, leaving no room for 5. So 5 must sit in the center. The remaining cells fall to the question "how much is this line still missing?", crossed out one by one. If you enjoy such puzzles, the Tower of Hanoi is another classic training ground.

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Quick quiz

↺ Try again

1. 1. All three box labels are wrong. Which box do you draw from?

   The one labeled “apples”The one labeled “oranges”The one labeled “mixed”

2. 2. You drew an apple. What does the box labeled “oranges” contain?

   OrangesApplesThe mix

3. 3. “Finish your homework and you get ice cream.” Homework was not finished — what about the ice cream?

   Definitely noneDefinitely someEither way, no promise is broken