It's Child's Play

Number Theory Level 4

A primary school math teacher gave her class the following problem.

\(\large{\square}+\large{\square}+(13 \times \large{\square}/\large{\square})+(12 \times \large{\square})+(\large{\square} \times \large{\square} / \large{\square})-\large{\square}=87\)

The blanks have to be filled with the natural numbers \(1\) to \(9\), with no repetitions.

All students are aware of the concepts of addition, subtraction, multiplication, division and the order of operations. However, they are yet to be introduced to the concept of fractions.

Every student in the class came up with a valid solution. However, no two solutions were the same. What is the maximum number of students in the class?

HINT : Since the students are unaware of fractions, none of the solutions would involve operations that result in fractions, when the operations are performed left to right.


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