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To determine the largest of three numbers in pseudocode, you can use the following logic:

if (num1 >= num2) and (num1 >= num3) then
    largest = num1
else if (num2 >= num1) and (num2 >= num3) then
    largest = num2
else
    largest = num3

This structure checks each number against the others and assigns the largest value to the variable largest.

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