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Consecutive odds and evens

Choose four consecutive odd counting numbers. Take the product of the middle two numbers and subtract the product of the first number and the last number. Try a few samples and formulate a rule. Explain why the rule works.

 Extensions

 What would happen if you used four consecutive even counting numbers in the above problem? Would your rule change? If so, find a new rule, and explain why this new rule works and why it is different from the original rule. If the rule does not change, does your explanation change? What would happen if you used four consecutive counting numbers in the above problem? Would your rule change? If so, find a new rule, and explain why this new rule works and why it is different from the original rule. If the rule does not change, does your explanation change?

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