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Named Products

Stage: 4 Short Challenge Level: Challenge Level:1

If we rewrite the equation we get the product $E\times I\times G \times H\times T  = T\times W \times O\times F\times O \times U \times R$.

There are $10$ different letters here, so each number from $0$ to $9$ must be represented by one of the letters. So one letter is $0$. Any product where this letter appears is $0$. Hence both sides must include this letter. The only letter on both sides is $T$.
Hence $T=0$ and the product $T\times  H\times R \times E \times E =0$.

This problem is taken from the UKMT Mathematical Challenges.