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Seventy six words start with HE, and two letters tie for the lead in the third box.
Each takes the third box in thirteen of the seventy six, seventeen percent apiece, with L on eight and M and N on six each. Eighteen letters appear there in total.
HEART, HEAVY, HEADS, HEARD and HEALS all come from the A branch, and every one is an ordinary word. That is a far better hit rate than the R branch manages, which holds HERBS, HERDS and HERON alongside several obscure entries.
HELLO, HEDGE, HEFTY, HENCE and HELIX are the useful entries elsewhere. HELLO in particular shares almost nothing with the A branch, which makes it a good second guess.
S closes twenty seven of the seventy six, thirty six percent, which is very high, with Y on eleven.
So ruling out a plural is the biggest cut available. Nine words repeat a letter, mostly the doubled E and doubled L of HEEDS and HELLS.
Both are common and they differ in two boxes. HEART tests the R fourth box and the T ending, neither of which HEAVY covers.
Twenty seven, which is thirty six percent. That is more than a third of the page on one letter.
A serf in ancient Sparta. It sits in the L branch with HELLO and HELIX and turns up in crosswords more than in speech.