Is this Number Theory?

Algebra Level pending

In the picture below, there are \(40\) red frogs on the left and \(50\) green frogs on the right and a empty space in the middle. The goal is to get all red frogs to the right and all green frogs to the left with a blank space in between. Red frogs are only allowed to move right and green frogs are only allowed to move left. Here are the kinds of moves:

  1. Slide This is when any color frog moves one space to an empty space. This is considered one move (example in picture).

  2. Jump This is when a frog jumps over another frog that is not the same color as the jumping frog. You are only allowed to jump over one frog, and the jumping frog has to land in a blank space. This is also considered one move (example in picture).

What is the least amount of moves it takes to achieve the goal?

Like this problem if you proved it! Don't forget to post a solution!

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