Game with Doritos

In a bag of Doritos, there are 2020 tortilla chips--1010 of which are BBQ flavored and the other 1010 are Nacho Cheese flavored. On the \(n^\text{th}\) second,

  • Anqi takes a chip from the bag, labels it \(n\), and places it on a plate. (She won't be able to tell which flavor the chip is until it's out of the bag.)
  • She can then decide to eat two (and only two) chips from the plate subject to the condition that they must be the same flavor. When she eats 2 chips labelled \( x \) and \( y \), she gets \( | x - y | \) jellies.
  • Alternatively, she can wait for a more opportune time to eat the chips. (But she can only eat two chips each second, so don't wait too long.)

Anqi does this for a total of 2020 seconds. What is the minimum number of jellies Anqi is guaranteed to get?


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