# 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), forming an exponent towers? . Over all $4!=24$ possible arrangements, let $S$ be the minimal value that is achieved. How many arrangements of these numbers would produce the value of S?

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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