I believe, it’s relatively easy to draw up a table and prove that there are dead ends given there’s only one, what I like to call, transit point, namely MM-NM-MN which yields a success. The last leg of the journey is to prove that the second branch off MM (patriarch) can only be TM, and that’s not too hard as we arrive at contradictions following other pathways, i.e. KM and BM.

I wish there was a pearl here from number theory which would prove this on an abstract level dealing with pure numbers.

Besides, I got problem 2 wrong and later read the answer. I’m loath to admit but I fell for the same line of reasoning as your students did.

]]>MM is the patriarch of the family. His suns are NM & TM. NM is the father of AN & MN, TM is the father os NT & KT. AN is not a father, MN is the father of BM & KM, NT is not a father and KT is the father of GK & NK

]]>and the solution is:

NM

MM

Just to double check (because I gave these to one of my math classes) — in Problem 4, is there any chance that the word “melns” with black lion is really supposed to be “melnas”?

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