Strings in the MIU System

Logic Level 1

In the MIUMIU system, you always start with the string MIMI and then form new strings by applying any of following rules any number of times:

RulesExamples
1. If your string ends with II, you can add a UU at the end.MIMIUMI\longrightarrow MIU
2. You can double the entire string following M.M.MIUMIUIUMIU\longrightarrow MIUIU
3. Three consecutive II's can be replaced with a single U.U.MIIIUMUUMIIIU\longrightarrow MUU
4. Two consecutive UU's can be removed from the string.MUUMMUU\longrightarrow M

Which of the following strings can be derived from MIMI using these rules?

Note: None of the rules can be used in the opposite way; for example, you aren't allowed to derive MUUIMUUI from MIMI by using a reversed version of rule 4.


Source: The MIUMIU puzzle was introduced by Douglas Hofstadter in his magisterial work Gödel, Escher, Bach.

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