answer:The mayor, whose name is Tom Harris, appears to be in his mid-to-late fifties, with a rounded face and a gentle smile. He has a thick head of graying hair, combed neatly to one side, and a pair of wire-rimmed glasses perched on the end of his nose. He's dressed in a simple, yet well-pressed, white dress shirt with a burgundy tie, giving off an air of quiet professionalism. Mayor Harris has a bit of a paunch, which speaks to his love of good food and perhaps a slightly sedentary lifestyle. However, his eyes sparkle with a genuine warmth and interest, and his mannerisms convey a sense of sincerity and approachability. He exudes the kind of down-to-earth, small-town charm that puts people at ease, which I imagine has served him well in his role as mayor. As we sit down to talk, I notice that his desk is cluttered with papers, pens, and a few framed photos of his family. There's a faint scent of fresh coffee wafting from the cup on his desk, which suggests he's a man who values his morning routine. Overall, Mayor Harris strikes me as a kind, capable, and dedicated public servant who genuinely cares about the well-being of his community.

answer:I smile and thank the mayor for the offer of coffee, That's very kind of you, Mayor. I'd love a cup. As he heads to the coffee maker, I take the opportunity to respond to his question. To be honest, Mayor, I've been really impressed with the town so far. The people have been incredibly welcoming, and I've enjoyed getting to know the officers at the department. They're a great team, and I'm looking forward to working with them. As for the transition, it's been relatively smooth. I've been trying to drink from a firehose, so to speak, learning as much as I can about the town and the department in a short amount of time. But everyone's been very helpful, and I'm starting to feel like I'm getting my bearings. I pause for a moment, taking the opportunity to ask the mayor a question. I have to say, Mayor, I've been struck by the strong sense of community here. Everyone seems to know each other, and there's a real feeling of camaraderie. What's the secret to that? Is it just the small-town atmosphere, or is there something more to it? The mayor returns with a steaming cup of coffee and hands it to me, and I take a sip, savoring the rich flavor.

answer:To find the smallest n such that f(n) = 50, we first need to analyze the constraints imposed by the function f(n). Since f(n) is the sum of the squares of the decimal digits of n, we know that each term in the sum is less than or equal to 9^2 = 81, as 9 is the largest possible decimal digit. Given that f(n) = 50, we are likely dealing with a number n with relatively few digits, as the sum of squares needs to be kept low. A single digit squared cannot produce 50, so n must have at least two digits. Considering two digits, the maximum possible value of f(n) without having any digit greater than 7 is 7^2 + 7^2 = 98, which is too high. With digits up to 6, the maximum possible value is 6^2 + 6^2 = 72, which is still too high but closer to our target of 50. We should consider combinations that might produce 50. Examining pairs of squares less than or equal to 6^2, we notice that 1^2 + 7^2 = 50. However, we aim to use the smallest n, so we consider an alternative: 5^2 + 5^2 = 50. This leads to the smallest n with f(n) = 50, which is n = 55. Therefore, the smallest n such that f(n) = 50 is n = 55.

answer:To find the smallest n such that g(n) = 50, we factor 50 into possible products of decimal digits. Since the digits are integers from 0 to 9, and we are looking for the smallest n, we want to minimize the number of digits used. The prime factorization of 50 is 2 * 5^2. Since we are looking for the smallest n, ideally we want to use only two digits, but the only possible combination would be 1 * 50 or 2 * 25, neither of which is suitable since 50 and 25 are not single-digit numbers. Considering three digits, we can directly use the prime factors: 2 * 5 * 5 = 50. This gives us the smallest n with g(n) = 50, as we have minimized the number of digits used. Therefore, the smallest n such that g(n) = 50 is n = 255.