Final answer:
The number of modules for version 4 can't be determined without additional information on the growth pattern from version 1. In mathematics, a linear or exponential pattern requires a common difference or multiplying factor, respectively, to calculate further terms in a sequence.
Step-by-step explanation:
You've asked about the number of modules for version 4, given that version 1 has 21x21 modules. Assuming that each version increases by a consistent size and knowing that version 1 is 21x21, we need more information to determine the exact size of version 4. Typically, in a sequence or pattern of numbers in mathematics, we would look for a common difference or a multiplying factor that consistently applies from one version to the next. Without additional details about the pattern of increase from version 1 to version 4, we cannot accurately calculate the number of modules in version 4.
If there is a specific pattern that applies that you haven't mentioned, please provide this information, and I can help you find the solution. If the number of modules grows linearly (by adding the same number of modules each time), you would add this number three times to the original 21x21 to get the modules for version 4. If it grows exponentially (multiplying by a constant factor each time), then you would multiply 21x21 by this factor three times.