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SMO 2016 Junior Round 1 Question 1

SMO · SMO 2016 Junior Round 1

Question 1

We know that $\mathrm{I}^2=\overline{\mathrm{ME}}$ and $\mathrm{I}^3=\overline{\mathrm{YOU}}$. If each distinct letter represents a unique digit such that the arithmetic holds, what is the value of $\mathrm{E}$?
  1. $4$
  2. $5$
  3. $6$
  4. $8$
  5. $9$