# Raising Squares Part 1

Logic Level 1

$\LARGE \square^{\square^{\square^{\square}}}$

You are given that the numbers $$1,2,3,4$$ are to be filled in the square boxes as shown above (without repetition). Of all $$4!=24$$ possible arrangements, find the total possible arrangements of these numbers such that the resultant number is a minimum.

Details and Assumptions

As an explicit example, a possible value of the resultant number is $$\large 2^{3^{1^4}} = 8$$.

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