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Omni-MATH / There are 100 piles of 400 stones each. At every move, Pete chooses two piles, removes one stone from each of them, and is awarded the number of points, equal to the non- negative …

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problem

There are 100100 piles of 400400 stones each. At every move, Pete chooses two piles, removes one stone from each of them, and is awarded the number of points, equal to the non- negative difference between the numbers of stones in two new piles. Pete has to remove all stones. What is the greatest total score Pete can get, if his initial score is 00? (Maxim Didin)
Plain-text mathematical notation (without MathML)
There are 100 piles of 400 stones each. At every move, Pete chooses two piles, removes one stone from each of them, and is awarded the number of points, equal to the non- negative difference between the numbers of stones in two new piles. Pete has to remove all stones. What is the greatest total score Pete can get, if his initial score is 0?

(Maxim Didin)
Original LaTeX notation
There are $100$ piles of $400$ stones each. At every move, Pete chooses two piles, removes one stone from each of them, and is awarded the number of points, equal to the non- negative difference between the numbers of stones in two new piles. Pete has to remove all stones. What is the greatest total score Pete can get, if his initial score is $0$?

(Maxim Didin)

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