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five six seven eight nine
I think the correct answer is 8
The "H" needs3 toothpicks to be drown, the "A" needs3, and the "T" needs2 =>3 +3 +2 =8
If some one has food stuck in their teeth and not able to spell HAT then they can use one. As its spelled from mouth why would someone spend lot of time to arrange tooth pick to write HAT. And your question says spell so its not writing with toothpick. correct?
To spell the word you don't need toothpicks.
Eight is the answer
8 Eight
7(seven)
Six
8 Toothpicks