Cloudy with a chance of meatballs

Question

I discovered that I can control the local weather, depending on what color shirt and hat I wear at a given location. My home country of Flanmanistan has hired me to go back and do drought and famine relief. I never know which combination of shirt and hat will deliver which weather at a new location, because each location has a different formula. So I wear a different shirt and hat combo each day, and I fill in a grid to keep track. For example, when I wore a green shirt and purple hat, the weather became cloudy. Tomorrow, I’ll finish the grid, but I can see the pattern already. What will be the weather when I wear a blue shirt and a white hat?

Hint 1: I ask that you use decimal math.

Hint 2: My choice of weather labels is not very important. "Rain" could be changed to "Showers", "Sardines" could be changed to "Chips", etc.

Update: Hint 3: The country name (my beloved Flanmanistan) and the concept of hats and shirts are not important. Look for a way to map each color combo to one of the five weather conditions. The process is fairly simple, once you know it. Notice that Yellow and Orange produce the same weather, so something about those two colors maps the same way.

Shirt ↓ Hat →	Black	White	Purple	Gold	Silver
Red	Sun	Sun	Meatballs	Meatballs	Rain
Green	Sardines	Sun	Cloudy	Meatballs	Rain
Blue	Meatballs	?	Sardines	Sardines	Sun
Yellow	Rain	Sardines	Sun	Cloudy	Meatballs
Orange	Rain	Sardines	Sun	Cloudy	Meatballs

CSV version:

Shirt Hat,Black,White,Purple,Gold,Silver
Red,Sun,Sun,Meatballs,Meatballs,Rain
Green,Sardines,Sun,Cloudy,Meatballs,Rain
Blue,Meatballs,?,Sardines,Sardines,Sun
Yellow,Rain,Sardines,Sun,Cloudy,Meatballs
Orange,Rain,Sardines,Sun,Cloudy,Meatballs

Another CSV version:

Shirt,Hat,Weather
Red,Black,Sun
Red,White,Sun
Red,Purple,Meatballs
Red,Gold,Meatballs
Red,Silver,Rain
Green,Black,Sardines
Green,White,Sun
Green,Purple,Cloudy
Green,Gold,Meatballs
Green,Silver,Rain
Blue,Black,Meatballs
Blue,White,?
Blue,Purple,Sardines
Blue,Gold,Sardines
Blue,Silver,Sun
Yellow,Black,Rain
Yellow,White,Sardines
Yellow,Purple,Sun
Yellow,Gold,Cloudy
Yellow,Silver,Meatballs
Orange,Black,Rain
Orange,White,Sardines
Orange,Purple,Sun
Orange,Gold,Cloudy
Orange,Silver,Meatballs

Answer 1

The answer is

Meatballs

It's hard to put your finger on a definite algorithm for this. The puzzle is labeled "calculation" and hint #1 urges you to use decimal math, however no numbers at all are provided. I was tempted to count the number of letters or add up the value of vowels / consonants in words for some kind of calculation, but other hints said words weren't important so that isn't going to work. Assigning random numbers to colors / weather patterns is also questionable as many different calculations can be obtained just by virtue of switching what you are assigning to each color. In the end, staring at the grid I did see a pattern emerge, and I am reasonably sure that this answer is correct.

Hint 3 pointed us to look at the similarities between Yellow and Orange, and that is an important observation, as that paints the way to other observations that are in the same style. Before we get to that though, one thing that needs to be observed is that Yellow and Orange display all 5 weather patterns, as does Green, but not Blue or Red.

Second observation to make is that Green not only displays all 5 weather patterns but also it is in the same order as Yellow, except shifted to the left by 1.

Third observation is that Red displays the same order of weather patterns as Green, except that Gold replaces Purple weather and White replaces Black weather.

Now putting it all together:

Just as Yellow and Orange have similarities - in that they are the same - Blue has similarities to all the other colors. It is similar to green, but instead of the weather pattern order being shifted left by 1 from Yellow, in Blue case they are shifted to the right by 2. Also Blue is similar to Red, in that Gold replaces Purple and White replaces Black. The weather pattern on Blue shirt days would have been "Cloudy, Meatballs, Rain, Sardines, Sun" without the Red substitutions.

So the missing weather on a Blue shirt / White hat day is Meatballs.

Answer 2

Amorydai gave the correct answer, using a method that seems to parallel my intended solution, so I have accepted Amorydai’s answer.

Here is my intended solution:

This “Hint 1: I ask that you use decimal math” was a hint to do the following:

Use decimal ascii values. “Ask” is a hint for “ascii”.

You can calculate the weather values as follows:

1) Take the first letter of each color combo. For example: Red and Black => R and B

2) Take the decimal ascii codes of #1 and add them together. For example: 82 + 66 = 148

3) Take the last digit of #2. For example: 8

4) Map from #3 to a weather value as follows. For example 8 maps to “Sun”

0 or 1 => Cloudy
2 or 3 => Meatballs
4 or 5 => Rain
6 or 7 => Sardines
8 or 9 => Sun

So Yellow and Orange shirts + a given hat color, will always map to the same weather value because

Y and O have decimal ascii values (89 and 79) which differ by 10

Here is the grid with the expanded math:

$\textbf{Weather Control Grid for Flanmanistan:}$ \begin{array}{|c|c|c|c|c|} \hline \textbf{Shirt$\downarrow$ Hat $\rightarrow$}&\textbf{Black}&\textbf{White}&\textbf{Purple}&\textbf{Gold}&\textbf{Silver} \\ \hline \textbf{Red}&82 + 66 = 148 => 8 => Sun&82 + 87 = 169 => 9 => Sun&82 + 80 = 162 => 2 => Meatballs&82 + 71 = 153 => 3 => Meatballs&82 + 83 = 165 => 5 => Rain \\ \hline \textbf{Green}&71 + 66 = 137 => 7 => Sardines&71 + 87 = 158 => 8 => Sun&71 + 80 = 151 => 1 => Cloudy&71 + 71 = 142 => 2 => Meatballs&71 + 83 = 154 => 4 => Rain \\ \hline \textbf{Blue}&66 + 66 = 132 => 2 => Meatballs&\color{red} {66 + 87 = 153 => 3 => Meatballs}&66 + 80 = 146 => 6 => Sardines&66 + 71 = 137 => 7 => Sardines&66 + 83 = 149 => 9 => Sun \\ \hline \textbf{Yellow}&89 + 66 = 155 => 5 => Rain&89 + 87 = 176 => 6 => Sardines&89 + 80 = 169 => 9 => Sun&89 + 71 = 160 => 0 => Cloudy&89 + 83 = 172 => 2 => Meatballs \\ \hline \textbf{Orange}&79 + 66 = 145 => 5 => Rain&79 + 87 = 166 => 6 => Sardines&79 + 80 = 159 => 9 => Sun&79 + 71 = 150 => 0 => Cloudy&79 + 83 = 162 => 2 => Meatballs \\ \hline \end{array}