The definition of the question is simple. The question is

*
How can we calculate
a number with four "4"s?*

Here, we can use four "4"s and mathematical symbols except numbers. For example, we can calculate 124 as follows

with four "4"s. Although we can use any kind of mathematical symbols, the difficulty of the problem would vary as depending on the limitation in the choice of mathematical symbols. We classify the limitation by points as the difficulty in the next section 2. Examples of the expressions for several numbers are presented in a section 3. As a succeeding question, do we have a general equation which expresses any non-negative integer ? This is discussed in the last section 4.