List of Eliminated Mega Stove Combos: Updated 9/2/11 10:00 PM KinzTime

[KeyLargo]

Originally Posted by GFred

Since the new Mega Stove uses 5 ingredients, there will be a lot more combinations. Given that there are 101 different food items in the W-Shop, there should be 79,208,745 different combinations. That's compared to a regular stove that take 3 ingredients and would have 166,650 different combinations. I haven't had time to figure out exactly how much KC it would cost to try every combination but if we assume that the average price of a food item is 5KC and each recipe takes 5 ingredients, that would mean the average recipe would cost 25KC so that would mean trying out every combination would cost around 1,980,218,525KC. That's a lot of KC.

How are y'all coming up with the number of different combinations? Just curious because it seems as if number would be lower in one way at least because it is a five food recipe.

[GFred]

Originally Posted by KeyLargo

How are y'all coming up with the number of different combinations? Just curious because it seems as if number would be lower in one way at least because it is a five food recipe.

It's a math formula. It's the same formula used to calculate simple LOTTO odds. With LOTTO, you have to, let's say, choose 6 numbers out of a pool of 40 numbers so there are 3,838,380 possible combinations. As for the Mega Stove recipes, you have to pick 5 ingredients out of a pool of 101 ingredients. That's why there is such a high number of combinations. Notice that I am talking about combinations and not the odds of finding a legitimate recipe. If there are many legitimate recipes, then the odds of finding one would be higher than one out of 79,208,745.

[ClaraZ25]

Look below for Cocoa's explanation of the math.

[GFred]

Originally Posted by ClaraZ25

The way I learned to calculate the number of different combos is by multiplying the # of different foods (93) by the exponent of how many times it is used for instance in the Mega Stove it would be 93^5 or 6,956,883,693 combination. But this number is not correctly accurate either as it includes combos like Almonds, Almonds, Almonds, Almonds, and Apple. The difference between my calculations and your is that mine does not include Almonds, Apple, Apple Juice, Cookies, and Fish Sticks and Apple, Apple Juice, Almonds, Fish Sticks, and Cookies as 2 different combos but your does.

The formula I am using should not include the same combinations in different orders. Using the LOTTO analogy again, whether you get 1-2-3-4-5-6 or 6-5-4-3-2-1 in LOTTO, you still win so the formula does not count these as two different combinations.

[Elephant]

When the order matters it is a permutation. LOL.
I haven't got the KC to try even one combo.

[KeyLargo]

Thanks; I figured it was a lotto type computation so now trying to figure out why it SEEMS {to me} as if it should have lower odds of getting/doing/finding than the 3 -- because after all there are less combinations overall because still same number of foods {usable ones of course} with one needing 3 types and other needing 5. Brain block, should go away...yep, anytime time now, it'll clear up...anytime now.... LOL

[cocoabean]

It is a lotto type formula... for COMBINATIONS... not PERMUTATIONS...

There are 64,446,024 combos for the Mega Stove and for the regular appliances there are 147,440 possible combination for each appliance...

The formula you should be using is...

...n!...
r!(n-r)!




From my original post... HERE

or in the spoiler below!

Spoiler: show

There are only 97 usable W Shop foods.


OK.... now for some math... You are using a permutation without repetition caluculation when you need to be using a combination without repetition calculation... keep reading!

Set - n=97, subset r=5

Now... here is the formula you should be using...

...n!...
r!(n-r)!

which shows that for the regular appliances there are 147,440 possible combination for each appliance... and for the megastove 64 million. (oops edited to 64 million!!!)


"Combinations" gives the number of ways a subset of r items can be chosen out of a set of n items. "Permutations" makes the same calculation, but in this case different arrangements of the same items are also counted.
For example, for a deck of cards n=52. There are 22100 ways that 3 cards can be chosen (nCr when r=3), but 132600 ways if it matters what order they are drawn in (nPr when r=3).

This spoiler is a rather obnoxious example of how this applies to cooking in ww...

Spoiler: show
Ok here's an example... remember... Once you've used your 4th food in this example with everything else in your first group you won't use them again with the other 96 foods and so on... Check out the link to my "how to help solve secret recipez" thread in the spreadsheet method section for a little more info on this... So, ok...your first combo with apples as food #1 and apple juice, almonds & bananas as foods 2,3,4 will produce 93 gunks. Your second elimination will not use your "4th food" at all... you'll use say asparagus as your "4th food" so when you go to blend apples, apple juice, almonds & asparagus with everything else "ee" you won't use bananas since you already did bananas & asparagus when bananas was your 4th food... so this combo will only produce 92 gaks when you do it with everything else... and so on... and once you change your "4th food" to a different one your next combo will produce 91 gunks let's say you change your 4th food to say bagel... because you've already done banana with bagel in your first combo and asparagus with bagel in your second combo you won't repeat them. Now let's say I'm doing a different combo with apples... say apples, apple juice, bananas, eggs, + ee... so when I get to doing apples, apple juice, bananas, eggs AND ALMONDS... I already did that combo when I did apple, apple juice, almonds bananas + ee... It's very confusing... but if you look at the example below regarding the lottery it will make more sense I think... so below is the lottery example and also a link to a calculator which will do the math for you.




The formula you are using is for permutations without repetition... that formula is for the number of arrangements 97 objects can be in... you need to alter the formula to reflect that order doesn't matter! Check this link for more info! Combinations and Permutations


Calculator...
Combinations and Permutations Calculator



Another example... (remember, like the lottery, order does not matter!)

Let's pretend we are trying to win a lottery... there are 97 numbers (foods) in the lottery and we need to pick the correct 5 numbers (foods) to win...






You want to calculate your odds at winning the lottery given:

• You must choose a sequence of 5 numbers correctly to win.
• The lowest number you can choose is 1
• The highest number you can choose is 97
• A given number can only be chosen once per try (per lottery ticket, etc.)

When you select your 1st number, you have 97 numbers to choose from, and...

...a 1 in 97 chance of picking the right one. (Mathematically, 1 in 97 is represented by the numerical fraction 1/97 or 0.010309.)

When you select your 2nd number, you have 96 numbers to choose from, and...

...a 1 in 96 chance of picking the right one. (Mathematically, 1 in 96 is represented by the numerical fraction 1/96 or 0.010417.)

When you select your 3rd number, you have 95 numbers to choose from, and...

...a 1 in 95 chance of picking the right one. (Mathematically, 1 in 95 is represented by the numerical fraction 1/95 or 0.010526.)

When you select your 4th number, you have 94 numbers to choose from, and...

...a 1 in 94 chance of picking the right one. (Mathematically, 1 in 94 is represented by the numerical fraction 1/94 or 0.010638.)

When you select your 5th number, you have 93 numbers to choose from, and...

...a 1 in 93 chance of picking the right one. (Mathematically, 1 in 93 is represented by the numerical fraction 1/93 or 0.010753.)

In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply.
So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.
1/97 × 1/96 × 1/95 × 1/94 × 1/93 = 1/7733522880
So, at this point, your odds of winning are 1 in 7733522880. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 5 numbers can be written down, which for 5 numbers is 5! (5 factorial) or 120. Divide 7733522880 by 120 to account for this, to get 64446024. In other words, there are 120 different ways that the 5 numbers you choose can be filled out on your lottery ticket--if you choose your 5 numbers correctly, any of these ways will make a winning ticket.

That's it! You have a
1 in 64,446,024
chance of winning the lottery you described.

[crazycat777]

Tried:
Ice Cream
Carrots
Bagel
Mushrooms
Lollypop

Outcome:
MegaGunk


Tried:
Almonds
Apple
Apple Juice
Asparagus
Bagel

Outcome:
MegaGunk


Tried:
Mushrooms
Eggs
Bread
Carrots
Cherries


Outcome:
MegaGunk


Tried:
Pineapple
Dragon Fruit
Tomato Soup
Lollypop
Cupcake

Outcome:
MegaGunk

[yummy98]

This is something you should eliminate lollipop, cherries, bananas, apple, popsicles= MEGAGUNK

[ClaraZ25]

Everyone Tara is only recording complete combos. Ing 1 + Ing 2 + Ing 3 + Ing 4 + Every Other Ingredient in the W-Shop. If you just have a partial combo please record that on the thread dedicated to the recipe you are trying to solve.