Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.3 Junior Find the answer

If $\odot$ and $\nabla$ represent different positive integers less than 20, and $\odot \times \odot \times \odot = \nabla$ , what is the value of $\nabla \times \nabla$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

If $\odot = 2$ , then $\nabla = \odot \times \odot \times \odot = 2 \times 2 \times 2 = 8$ , which is possible. Thus, $\odot = 2$ and so $\nabla = 8$ . This means that $\nabla \times \nabla = 8 \times 8 = 64$ .

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