We know that after the plague of the firstborn, Pharaoh finally gives in and sends the Jews out from Egypt. Why did it take 10 plagues? One reason, of course, is that he kept hardening his heart and being stubborn. But it’s weird — he always seemed to forget about all the plagues that already happened. Why did he not learn his lesson?
Pharaoh might have also been thinking mathematically. That is, he thought each plague was the last plague. That meant that each new plague was a smaller fraction of the plagues than any previous plague. For example, after the third plague, any additional plague was at most a third of all the plagues he experienced so far. That might not seem too bad and so he decided to take another plague. Well, that is until the hardest plague of the firstborn.
We know now that there were 10 plagues in the end. That means that we can think of the whole unit and compare how many plagues were really left to how many happened already. What’s the last plague that afterwards you could still tell Pharaoh that he had over half as many plagues to experience as he already went through?
Solution: This would be after the sixth plague, boils. After this plague, there were four plagues remaining and 4/6 is greater than a half. After the seventh plague, there were three remaining and 3/7 is less than a half.
Ari Blinder is a math educator living in Highland Park and the owner of Math for the Masses, an innovative math tutoring and consulting company. For more information, visit www.math4masses.com. Ari can be reached at ari.m4m@gmail.com.