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Seventy four words start with ME, and R takes the third box more often than anything else.
R takes it in fourteen of the seventy four, nineteen percent, with T on twelve, A on ten and S on eight. Sixteen letters appear there in total.
That is a wide spread with a modest leader, so the third box narrows the page without deciding it.
MEDIA, MEANS, MERCY, MEANT and MEDAL are the entries a puzzle is most likely to want, with MERIT, MELON and MEANS behind them.
METAL, METER, METRE, METRO and METED all sit on one short stem and several differ by a single letter. METER and METRE are the same word spelled two ways and both appear here, so confirm the fourth box before committing.
S closes twenty three of the seventy four, thirty one percent, with E on ten and Y on eight. I and E tie for the fourth box at ten words each.
Both are common and they differ in three boxes. MERCY tests the R third box, which is the largest branch here.
Both appear on this list as spelling variants. They differ in the fourth and fifth boxes, so that is where the page decides between them.
Twenty three, which is thirty one percent. Ruling out a plural is the biggest single cut here.