I saw this puzzle when I was kid, in a Martin Gardner book. Back then it was an inch worm instead of an ant. When I saw the answer, it blew my mind at first. La

I saw this puzzle when I was kid, in a Martin Gardner book. Back then it was an inch worm instead of an ant. When I saw the answer, it blew my mind at first. Later I understood how it was related to the fact that the harmonic series diverges, and it became less mind blowing, but it's still a little mind blowing—because it's still a little mind blowing that the harmonic series diverges. It became one of my favorite puzzles, and I tried it on friends and family. I certainly never thought it could have "real-world" applications. But then it occurred to me, people were solving this puzzle every day. Think of an ordinary loan. Each month, you make a payment that's part interest and part principal. At first it's mostly interest, then the ratio shifts over time, the final payments being nearly all principal. You normally start with a loan amount (principal), an interest rate, and a loan duration (typically 180 or 360 months). From these parameters, you figure the monthly payment, a process called amortization. Part of the payment goes towards interest, part towards the principal. Each month you're required to service the loan, which means to pay (at least) the interest. That's the cost of renting the money. Some loan arrangements allow you to pay down the principal at your own pace. If you only ever pay interest, the principal will remain unchanged, and the loan will go on forever. This is the Netflix model: they don't care how long you keep a disc—you're paying rent on it every month. Many people pay more than the monthly payment from time to time. The principal will be reduced by this extra amount. The worm has taken out a loan. The twist is, we don't yet know the principal, nor the total amount to be paid, which corresponds to the final rope length. Instead, we know the payment: 1 yard. The interest portion varies, but the worm consistently pays down the principal 1 inch each pay period. Some of the added yard (monthly payment) appears in front of the worm (interest portion) some behind it (principal portion). Stretching the rope uniformly has the effect of servicing the interest. At first, most of the newly added rope appears in front of the worm, but as with the ordinary loan, the back/front ratio increases over time. That the worm will eventually reach the end of the rope is now evident. If your interest payment is taken care of, then even a small monthly pay-down of the principal will eventually pay off any size loan.