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N first and R third covers 38 words, and one of them is far more common than everything else put together.
O leads at about thirty two percent, A at twenty nine, E at twenty one and U at thirteen. On paper that is a fair spread.
NORTH, NURSE, NERVE, NORMS and NERDS are the entries in ordinary use. Almost everything else in the count is a rare or technical form.
That branch holds twenty nine percent of the words but hardly any of them are familiar, so a guess aimed at it will often burn a turn without helping.
NORTH is the guess to start with. It covers the largest branch and its T and H rule out a great deal when they miss.
NURSE is the sensible second, since it moves to the smallest branch while holding the only common word there.
NORMS and NORSE sit there too, though neither comes close to NORTH in everyday use.
NUR is not a productive opening in English. NURSE is effectively the whole branch, with the rest running to dialect forms.
They share four letters and differ in the last box, so landing either one closes out the E branch immediately.