Find the least number of coins required that can make any change from 1 to 99 cents

Question

Recently I challenged my co-worker to write an algorithm to solve this problem:

Find the least number of coins required that can make any change from

Answer 1

Here's a simple c# solution using Linq.

internal class Program
{
    public static IEnumerable Coins = new List
    {
        new Coin {Name = "Dime", Value = 10},
        new Coin {Name = "Penny", Value = 1},
        new Coin {Name = "Nickel", Value = 5},
        new Coin {Name = "Quarter", Value = 25}
    };
    private static void Main(string[] args)
    {
        PrintChange(34);
        Console.ReadKey();
    }
    public static void PrintChange(int amount)
    {
        decimal remaining = amount;
        //Order coins by value in descending order
        var coinsDescending = Coins.OrderByDescending(v => v.Value);
        foreach (var coin in coinsDescending)
        {
            //Continue to smaller coin when current is larger than remainder
            if (remaining < coin.Value) continue;
            // Get # of coins that fit in remaining amount
            var quotient = (int)(remaining / coin.Value);

            Console.WriteLine(new string('-',28));
            Console.WriteLine("{0,10}{1,15}", coin.Name, quotient);
            //Subtract fitting coins from remaining amount
            remaining -= quotient * coin.Value;
            if (remaining <= 0) break; //Exit when no remainder left
        }
        Console.WriteLine(new string('-', 28));
    }
    public class Coin
    {
        public string Name { get; set; }
        public int Value { get; set; }
    }
}