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IMSO 2022 Mathematics – International Essay Question 8

IMSO Science · IMSO 2022 Mathematics – International Essay

Question 8

There are 25 oranges, having different sizes, which are placed on a 5 by 5 grid. First, we take the biggest orange from each of the rows. Thus, we now have 5 oranges, and then among them, we locate the smallest one among these 5 oranges and mark it as X. After which, we place these 5 oranges back into their original positions. Similarly, take the smallest orange from each of the columns. After doing this, we again have 5 oranges, and then among them, we locate the biggest one among these 5 oranges and mark it as Y. After which, we again place these 5 oranges back into their original positions. Is it possible to determine which orange is bigger, X or Y? Justify your answer.