Question 10
The number “$11$” has a curious property where it can be expressed as the sum of a positive integer power of $2$ and a positive integer power of $3$ in two different ways, namely $11=2^3+3^1=8+3$ and $11=2^1+3^2=2+9$.
What is the smallest three-digit integer that has this curious property?
(Note: the positive integer powers of $2$ are $2^1=2$, $2^2=4$, $2^3=8$, $\ldots$, while the positive integer powers of $3$ are $3^1=3$, $3^2=9$, $3^3=27$, $\ldots$.)
What is the smallest three-digit integer that has this curious property?
(Note: the positive integer powers of $2$ are $2^1=2$, $2^2=4$, $2^3=8$, $\ldots$, while the positive integer powers of $3$ are $3^1=3$, $3^2=9$, $3^3=27$, $\ldots$.)