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Omni-MATH / 100 children stand in a line each having 100 candies. In one move, one of them may take some of their candies and distribute them to a non-empty set of the remaining children. Afte…

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problem

100100 children stand in a line each having 100100 candies. In one move, one of them may take some of their candies and distribute them to a non-empty set of the remaining children. After what least number of moves can it happen that no two children have the same number of candies?
Plain-text mathematical notation (without MathML)
100 children stand in a line each having 100 candies. In one move, one of them may take some of their candies and distribute them to a non-empty set of the remaining children. After what least number of moves can it happen that no two children have the same number of candies?
Original LaTeX notation
$100$ children stand in a line each having $100$ candies. In one move, one of them may take some of their candies and distribute them to a non-empty set of the remaining children. After what least number of moves can it happen that no two children have the same number of candies?

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