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There are many rules for that pair. Without further information about the kind of operators expected to be used it is impossible to give an answer.

Let me give you a very simple example:

What is the rule for input 2 output 4:

rule 1: x → x + 2

rule 2: x → 2x

rule 3: x → x^2

rule 4: x → x^3 ÷ 2

rule 5: x → x^3 - x^2

rule 6: x → x^3 - 2x

rule 7: x → x^3 - 4

rule 6: x → x^4 - x^3 - x^2

etc

Even with a list of permissible operators, there is no one definite answer given only one pair of input/output - it would require further examples of inputs and their corresponding outputs to be able to narow the possible answers: only slightly as it is still possible to find [infinitely] many polynomials that provide the given input/output pairs.

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Q: What is the rule for Input 456712 Output 0246?
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