# How to evaluate power towers?

Logic Level 3

$\Large 2 \; \underbrace{\square \; 2 \; \square \; \cdots \; \square \; 2 \; \square}_{n \text{ number of }\square\text{'s}} \; 2 = 2^{2^{2^{2^2}}}$

What is the minimum value of positive integer $$n$$ such that we can fill in the boxes above with the four mathematical operators ( $$+, -, \times , \div$$ ) and the equation holds true?

Note: Order of operations (BODMAS) applied.

Bonus: What would the answer be if we were to find the maximum value of integer $$n$$?

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