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Three times what number is no larger than two times that same number?

Why this works

This riddle plays with the relationship between multiplication and inequality. If we let the unknown number be represented by \( x \), the riddle states that three times \( x \) (which is \( 3x \)) is no larger than two times \( x \) (which is \( 2x \)). When we set up the inequality \( 3x \leq 2x \) and simplify it, we find that \( x \) must be less than or equal to 0. The only number that satisfies this condition while also making both sides equal is 0, as \( 3 \times 0 = 0 \) and \( 2 \times 0 = 0 \). Thus, the answer is indeed 0!

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Common Wrong Answers

“1”

If you multiply 1 by 3, you get 3, which is larger than 2 times 1 (which is 2), so this does not satisfy the condition.

“2”

Multiplying 2 by 3 gives 6, which is larger than 2 times 2 (which is 4), therefore it cannot be the correct answer.

“-1”

Multiplying -1 by 3 gives -3, which is indeed no larger than 2 times -1 (which is -2), but the riddle requires a number that satisfies the condition while also being the smallest number possible, which is 0.

Numbers

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