Seeking Optimal Strategy for Decimal Puzzle - Truncation and Lengthening to find unknown C

[williejradley]

I'm stuck in a fascinating number puzzle and seeking your help in solving it. Here's a quick rundown:


I have a decimal number A with a length of 88 characters and another decimal number B with a length of 87 characters. The multiplication of A by B
yields a lengthy decimal number C, with only the first 87 characters of C being essential.

Here are the specific values:

A: 3000160234650311700045165878204726433345536259833824023779560455187416495753135486956898
Given B (for reference): given B Range = 418784234900532787432789884236789i23000023407429873248794235767426732909040987664328765 ( The Actual B lies at a point below This )
Actual B value for work out: 389977570440151655940314858043173160372477129144525839890646472875452499155218446445464 (B+1)
C: 116999519924008385189380096562191943786959323801872795172325828894545913906482739587093... (long decimal)
Additional Considerations:

B lies within a given range but is unknown, only known to be below a certain point.
A can be lengthened and hold any value.
B should be truncated to only 8 digits.
Strategy for Known B Value:

Multiply the original B (389977570440151655940314858043173160372477129144525839890646472875452499155218446445464) by the original A.

Result: A product representing the original C.
Multiply the truncated B (38997757) by the original A.

Result: A product representing a truncated C due to B truncation.
Subtract the second product from the first product to find the difference caused by truncation.

Result: The difference that needs to be compensated for.
Divide the difference by the truncated B. This yields a number representing the "missing part" that needs to be added to A to compensate for the truncation.

Result: The missing part that, when added to A, will offset the truncation.
Add the missing part to the original A. This lengthened A will produce a product with the first 87 digits matching C when multiplied by the truncated B.

Result: Lengthened A, ready for precise multiplication.


Summary:

I have a puzzle where the product of a decimal number A (88 characters) and an unknown decimal number B (87 characters) results in a lengthy decimal C. The first 87 characters of C are crucial, and I know that C unlocks a puzzle. I have the value of A and a range for B below which will be Actual B for certain, but brute forcing through the long B range is time-consuming starting from the given B and going a step lower each time in which case we will meet actual b at a point. bruteforcing can be done if there is a way to truncate B to 8 digits and lengthen A by any length . We can even change the value of A as per our startegy it doesnt have to be the same A given but the first 87 digits of the result of mutiplication should match C to the precision no excuses.

I seek a method to make B shorter (8 digits or lesser) while ensuring that when multiplied by A(when C is unknown unlike the above strategy when C is Known) the first 87 characters of the result match C to precision. B can be decimal or without decimals (e.g., 0.38, 3.8, 38.9), and it needs to be found efficiently. The actual C value is unknown but is locked in a text file we can match the answer to see if it is correctbut there is no way of reading it or getting a clue .

I'm open to insights from various fields, such as logic, mathematics, cryptography, and arithmetic, to solve this puzzle in the shortest time possible with a code prefferably. The goal is to provide the correct answer to the puzzle by finding a B value that, when multiplied by A, produces a result with the desired precision.

I am particularly keen on optimizing this process, considering the constraints mentioned. If you possess any mathematical insights, algorithms, or
strategies or code that could expedite this procedure or shed light on the puzzle, your input would be highly appreciated.

Thank you for investing your time and expertise! Let's crack it.