Splitting Piles

Probability Level 1

You are given a set of cards arranged in a line. Each card is either black\color{#333333}{\text{black}} or red\color{#D61F06}{\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 black\color{#333333}{\text{black}} cards in the left part is exactly the same as the number of red\color{#D61F06}{\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 black\color{#333333}{\text{black}} card in the left part and 1 red\color{#D61F06}{\text{red}} card in the right part


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