How much harder does a problem get as its size grows? This experiment answers that question directly. A brute-force program that tests every possible combination of pennies, nickels, dimes, quarters, and half-dollars works for small amounts — but as the target value increases, it slows to a crawl. By searching for patterns in the results, you discover that the five-coin problem connects to simpler four-coin and three-coin problems. A new program built on those patterns runs over 26,000 times faster, solving the ten-thousand-dollar problem in less than an hour. That speedup is what choosing the right algorithm looks like in practice: a problem that seemed practically unsolvable becomes finished before lunch.