At this moment in the story, it is realized that Tessie Hutchinson is the ill-fated person who will be sacrificed in a longstanding tradition in this small village. She cannot even open her slip of paper herself, realizing her fate as the rest of her family opens papers that are blank, containing no black dot.
The determination of a person's entire fate in this village is created with a single black dot. The night before, Mr. Summers had sat in the coal company office and had chosen one slip of paper out of all those before him. Using a "heavy pencil," he had drawn a single black dot on this slip of paper and had placed it in with all the others for the lottery which the town would engage in the following day.
This dot would determine the death of one person in town. Although he couldn't predict which townsperson would select this slip of paper, Mr. Summers realized when he drew the dot that the following day, someone would select this exact slip of paper and then die because of that choice. It could be a child, and it could be Mr. Summers himself.
The pencil he uses as he draws the dot is therefore "heavy" because it ultimately delivers the outcome of death.
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