# 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?

×