It was my first day as a postdoc at MIT, and after landing at Logan Airport I took a taxi to a relative in Beverly, north of Boston, where I was going to stay for a few days while looking for a place to live for me and my family who were arriving a week later. The taxi driver had some difficulties locating the address and when we arrived the taximeter was on 34 dollars and fifty cents. “With the tip I will give you forty,” I told the driver and handed him a 100 dollar bill. “Sorry,” said the driver, “don’t you have smaller bills? I have only 40 dollars on me for change.” Hmm, I thought but could not find any small bills except for 10 notes of one dollar each. The problem seemed unsolvable. Can mathematics come to the rescue?
I had a brilliant idea: “Let me pay you 110 dollars instead of 100 and then you will have to give me back fifty dollars instead of sixty,” I told the driver. The driver immediately agreed and I handed him a one hundred bill followed by 1,2,3,…,10 single dollar bills. The driver gave me back two twenty dollar bills followed by 1,2,3,…,10 single dollar bills, and left. Hmm, I thought, how interesting! The ten dollar bills seemed to be precisely the same bills I handed the driver. This looked like a salient feature of my ingenious solution — the ten dollar bills served as a sort of mathematical catalyst, I put them in, and I got them out! It is nice to see how mathematics comes to the rescue, I continued to think for 2-3 more minutes.
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