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UKMT Junior Mathematical Challenge, 2022

Number theory Difficulty 1.0 Junior Find the answer United Kingdom

How many of the following take integer values? $\dfrac{1}{1}$ , $\dfrac{11}{1+1}$ , $\dfrac{111}{1+1+1}$ , $\dfrac{1111}{1+1+1+1}$ , $\dfrac{11111}{1+1+1+1+1}$

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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