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An excel approach to a BWS3 contest
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maf34100
Posts: 52,418 Level 5
in Discussions
@johamilton posted a contest to add five 5-digits scores and five 6-digits scores from level 409 and achive a sum of 1225445 points.
Lets generate 9 5-digits and 6-digits scores and look for the combinations of 9 numbers in groups of 5 numbers. The result is 126 combinations of each type of score. Then we calculate the sum of the 5 numbers in each combination.
We have 126 sums of 5-digits scores and 126 sums of 6-digits scores. If we place them in an spreadsheet we can have 126x126=15876 sums of 5-digits+6-digits scores to compare with the 1225445 points.
It is much simpler than it looks at the first reading. I know that @Lemurtek and @Kiki_g have the capabilities and to implement it so it is dedicated to you.
Guys attached is an implemetantion guide and I am waiting for your comments.
Comments
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Hello @maf it's not that easy either, according to my calculations there are 21,111,552 combinations and exactly 421 solutions.
To find the correct combinations you would have to write a macro. It might also work with formulas, but that would make the calculator work itself to death.
But I will try it.... 😎
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@Kiki_g every string will give the sum of 5 scores. We have 126x126=15876 combinations to achieve the desired sum with the use of the first batch of 9 5-digits and 6-digits score.
The reloading of excel with the 2nd batch of 9 5-digits and 6-digits is simple and quick. I did not make more than 3 reloads. How did you find the 21,111,552 combinations?
I don't use macros which may speed calculations.
If the excel is properly set up eveything else is easy and no time consuming. The only time required is to replay level 409 to generate the next batch. You can also mix scores from previous batches and reload the excel. I believe that you can easily set up the excel. I am available for more details on the excel formulas needed.
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Hi @maf the possible combinations only refer to the results I have achieved, I'll try to explain how I calculated it.
Actually, it's like Lotto (6 out of 49): 49x48x47x46x45x44/1/2/3/4/5/6 gives a chance of 13,983,816 for 6 correct ones, because just as many combinations are possible. I don't even know if you know that, I mean Lotto.
I have 8 5-digit results (first image) and 36 6-digit (the numbers in the first column from the left) results.
5 out of 36 is: 36x35x34x33x32/1/2/3/4/5=376,992 combinations
5 out of 8 is: 8x7x6x5x4/1/2/3/4/5=56 combinations.
376,992 combinations x 56 combinations equals 21,111,552 combinations.
5 out of 36 is: 36x35x34x33x32/1/2/3/4/5=376,992 combinations
5 out of 8 is: 8x7x6x5x4/1/2/3/4/5=56 combinations.
376,992 combinations x 56 combinations equals 21,111,552 combinations.
I wrote a macro for myself that only creates the possible combinations from the results I have achieved and that alone is 421.
Here is a picture of the first 170 results
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@Kiki_g reading your comment and looking at your screens I realized that from your 8 5-digits and the 36 6-digits scores your macro generated 421 bullseye combinations, if I am correct.
The macro you wrote did miracles. My question, your macro generates the 21,111,552 combinations and presented only the 421 correct ones?
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@Kiki_g this is what I used
https://www.calcfun.eu/calc-56-syndyasmos-n-arithmon.html
the 2nd part of the link looks like this
In the large square you type your 9 numbers separated with "," and in the small square you type 5.
You click the
and you get listing of your combinations provided that they are not more than 200
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