User blog comment:LittlePeng9/ITTM galore/@comment-10429372-20140323165401/@comment-1605058-20140323172331

Look at numbers 0-7 as binary strings. For example, 6 is 110, which means 0 on input tape, 1 on scratch tape, 1 on output tape. We don't switch tapes - we look at all of them at once. So yes, we need 4 colors for each output bit - other two tape cells can have 4 different states.