Can someone abuse LINQ and solve this money puzzle?

For the fun of it, I would like to see someone use and abuse LINQ to solve this money problem. I really have no idea how you would do it - I suppose Populating some set and then selecting off of it.

If given a total number of coins and give the total amount of all coins added together: Show every possible combination of coins. Coins are Quarters(.25), Dimes(.10) Nickels(.05) and Pennies(.01)

Include the option so that there can be zero of a type of coin or there must be at least 1 of each.

Sample Problem: If I have 19 coins and the coins add up to $1.56 and there must be at least 1 of every type of coin.

The answer would be:

1 Quarters, 9 Dimes, 8 Nickels, 1 Pennies

2 Quarters, 5 Dimes, 11 Nickels, 1 Pennies

2 Quarters, 9 Dimes, 2 Nickels, 6 Pennies

3 Quarters, 1 Dimes, 14 Nickels, 1 Pennies

3 Quarters, 5 Dimes, 5 Nickels, 6 Pennies

4 Quarters, 1 Dimes, 8 Nickels, 6 Pennies

5 Quarters, 1 Dimes, 2 Nickels, 11 Pennies

And if we allowed zero for a coint we allowed get an additional 0 Quarters, 13 Dimes, 5 Nickels, 1 Pennies

Here is some sample C# code using a brute force method to solve the problem. Don't bother improving the sample, let's just see a solution using Linq. //Try not to use any regualar c# looping code if possible.

private void SolveCoinProblem(int totalNumberOfCoins, double totalAmount, int minimumNumberOfEachCoin)
    {
        int foundCount = 0;
        long numberOfTries = 0;
        Console.WriteLine(String.Format("Solving Coin Problem:TotalNumberOfCoins={0}TotalAmount={1}MinimumNumberOfEachCoin{2}", totalNumberOfCoins, totalAmount, minimumNumberOfEachCoin));
        for (int totalQuarters = minimumNumberOfEachCoin; totalQuarters < totalNumberOfCoins; totalQuarters++)
        {
            for (int totalDimes = minimumNumberOfEachCoin; totalDimes < totalNumberOfCoins; totalDimes++)
            {