I beg to differ with your explanation. The real answer is only 3 pieces. He should have had two more pieces. You see only Litvaks spell קוגל with a vav - koogel. Everyone knows kugel is spelled קגל = eg 133. Of course, your parable suffered in the translation. You see, the original was not kugel, but chulent (or cholent if you're a Litvak). Then the Rebbe's answer made sense

dod