Background. No background -- math arguments should be settled strictly on the merits.
The question. If you doubled 1 penny every day for 30 days what number would you be closest to?
- $5 million
- $50 million
Analysis. Call the original penny “A.” On day one, you double it and have pennies A and B. On day two, double penny A again, producing penny “C.” You now have three pennies: A, B, and C.
On day three, double penny A again, producing penny D. You now have four pennies: A, B, C, and D. Continue the process till you have doubled penny A once a day for 30 days. You will have thirty-one pennies, A through EE. Thirty-one pennies is closest to $5,000, so the correct answer is “d.”
Objection. No, no, no. You have to double two pennies on day two, four pennies on day three, eight pennies on day four, and so on.
Response to Objection. If you do that, you are doubling more than one penny every day after day one, and the question requires that you “double 1 penny every day for 30 days.” The question was not, “If you multiply 1 by 2 on day one, and multiply each day’s product by 2 through day thirty, to what number is the final product closest?”
Real-World Relevance. You know who you are. Live long and prosper.