Splitting Piles

You are given a set of cards arranged in a line. Each card is either \(\color{black}{\text{black}}\) or \(\color{red}{\text{red}}\). You may divide the cards into two parts by picking a line before or after the whole cards (so that a part can contain 0 cards), or somewhere between two cards.

No matter how many cards are arranged in whatever manner, can you always ensure the number of \(\color{black}{\text{black}}\) cards in the left part is exactly the same as the number of \(\color{red}{\text{red}}\) cards in the right part?


An example split that fulfills the condition is shown below.

There is 1 \(\color{black}{\text{black}}\) card in the left part and 1 \(\color{red}{\text{red}}\) card in the right part

There is 1 \(\color{black}{\text{black}}\) card in the left part and 1 \(\color{red}{\text{red}}\) card in the right part

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