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    Author Topic: Bitcoin puzzle transaction ~32 BTC prize to who solves it  (Read 348566 times)

    • bcchanger
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    May 04, 2025, 08:35:20 PM
     #9881
    Quote from: Akito S. M. Hosana on May 04, 2025, 08:24:22 PM
    Quote from: nomachine on May 04, 2025, 08:06:08 PM
    Consult the crystal ball.  Grin

    I have one, but I don’t want to look at it. So, random mode is the best. The percentages are the same as the prefixes. There’s no connection anywhere here  Tongue



    A waste of time. Trust me, I’ve done tons of tests and confirmed that random can be fast (done this on low 44-bit ranges), but it can scan 4 times the entire range without a single result. That means duplication, and avoiding it completely is nearly impossible. Totally a waste of time.

  • Akito S. M. Hosana
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    May 04, 2025, 08:42:30 PM
     #9882
    Quote from: nomachine on May 04, 2025, 08:32:15 PM
    There is no best method—each one is good if you have enough hardware resources. If you don’t, none of them will work.  Wink

    So, the dude with 3000 GPUs always wins...  Tongue

  • bcchanger
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    May 04, 2025, 09:07:10 PM
     #9883
    Quote from: Akito S. M. Hosana on May 04, 2025, 08:42:30 PM
    Quote from: nomachine on May 04, 2025, 08:32:15 PM
    There is no best method—each one is good if you have enough hardware resources. If you don’t, none of them will work.  Wink

    So, the dude with 3000 GPUs always wins...  Tongue

    Focus on the game, not people . More resources more chances like mining..

  • Benjade
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    May 05, 2025, 12:34:21 AM
     #9884
    Quote from: bcchanger on May 04, 2025, 08:35:20 PM
    Quote from: Akito S. M. Hosana on May 04, 2025, 08:24:22 PM
    Quote from: nomachine on May 04, 2025, 08:06:08 PM
    Consult the crystal ball.  Grin

    I have one, but I don’t want to look at it. So, random mode is the best. The percentages are the same as the prefixes. There’s no connection anywhere here  Tongue



    A waste of time. Trust me, I’ve done tons of tests and confirmed that random can be fast (done this on low 44-bit ranges), but it can scan 4 times the entire range without a single result. That means duplication, and avoiding it completely is nearly impossible. Totally a waste of time.


    You can avoid duplication completely with a Feistel network. https://en.wikipedia.org/wiki/Feistel_cipher

  • Bram24732
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    May 05, 2025, 05:43:32 AM
     #9885
    Quote from: Akito S. M. Hosana on May 04, 2025, 08:42:30 PM
    Quote from: nomachine on May 04, 2025, 08:32:15 PM
    There is no best method—each one is good if you have enough hardware resources. If you don’t, none of them will work.  Wink

    So, the dude with 3000 GPUs always wins...  Tongue

    Not always haha, beauty of randomness !

  • AdamParker1985
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    May 05, 2025, 07:48:04 AM
     #9886
    Quote from: Benjade on May 03, 2025, 12:08:31 PM
    Quote from: Bram24732 on May 03, 2025, 12:01:54 PM
    Quote from: Benjade on May 03, 2025, 09:17:52 AM
    Quote from: Bram24732 on May 03, 2025, 06:58:22 AM
    Quote from: fantom06 on May 03, 2025, 05:13:19 AM
    Quote from: Bram24732 on May 03, 2025, 03:18:11 AM
    Quote from: bitcoinpuzzles621 on May 02, 2025, 10:53:09 PM
    whatever you all do, dont keep giving bram more of your code.  he already has 3000 computers and the rest of us might only be using two.  so giving away all of your code secrets to him will only make sure that the rest of us end up broke with no money when he uses that knowledge to solve every remaining puzzle.   dont say i never warned you when it happens.  lol   i do believe in some knowledge sharing though.  but he has too big of an advantage already over the rest of us.  just my opinion or thoughts. 

    I think I already said I’m not working on any puzzle now that they are no longer profitable.

    I sent you a scrypt, check your private messages

    Please do not send me generic AI generated scripts which don’t even make sense.

    I imagine you are aware that big data already uses AI for their code, as is the case with GitHub itself. Your reasoning is ridiculous. Whether it is code that comes out of AI or human, it is still code. It is the way it is worked that matters.

    I think you missed the important part : which don’t even make sense
    I don’t care if you use AI to make code as long as the code makes sense. All the code I received in my DM makes zero sense whatsoever.

    You have to be stupid to send you solutions, so it's logical that you receive stupid code.  Grin

    This whole back-and-forth is getting a bit wild. At the end of the day, it doesn’t matter if the code comes from AI or a human—if it doesn’t make sense, it’s not helpful. And yeah, sharing half-baked scripts just to say you contributed isn’t doing anyone any favors. If someone really wants to collaborate, at least make sure what you’re sending has some logic to it.

  • Akito S. M. Hosana
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    May 05, 2025, 08:18:59 AM
     #9887
    What’s up with this? Nobody dropped a Python script lately? Y’all running low on ideas or what?  Tongue

  • nomachine
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    May 05, 2025, 08:46:31 AM
     #9888
    Quote from: Akito S. M. Hosana on May 05, 2025, 08:18:59 AM
    What’s up with this? Nobody dropped a Python script lately? Y’all running low on ideas or what?  Tongue

    I have so many ideas—you wouldn’t even believe it. Half of ’em are junk. A few kinda work, but it really depends on the hardware. Python’s slow as hell. But hey, let me hook you up.


    This will sound a bit twisted - but the puzzle can be solved with the following formula


    Puzzle 65 as example:

    (√(2^64)/8192×Y)^2+2^64 = 30568377312064202855

    (√(2^64)/8192×6640.something)^2+2^64 = 30568377312064202855

    Given equation: ((sqrt(2^64)/8192 * Y)^2 + 2^64) = 30568377312064202855

    Simplify sqrt(2^64)
    sqrt_2_64 = 2**32

    Calculate divisor
    divisor = 8192  # = 2**13

    Simplify coefficient
    coefficient = sqrt_2_64 divisor  # = 2**19 = 524288

    Isolate squared term
    target = 30568377312064202855
    squared_term = target - 2**64  # = 12121633238354651239

    Take square root
    sqrt_term = 3481613620  # Approximate sqrt(12121633238354651239)

    Solve for Y
    Y = sqrt_term coefficient  # = 3481613620 524288 ≈ 6640.651

    All puzzles

    Code:
    from decimal import Decimal, getcontext

    # Set precision to 180 significant digits to ensure 100 decimal places after the decimal point
    getcontext().prec = 180

    # HISTORY list from the puzzle
    HISTORY = [
        (20, 863317), (21, 1811764), (22, 3007503), (23, 5598802), (24, 14428676),
        (25, 33185509), (26, 54538862), (27, 111949941), (28, 227634408), (29, 400708894),
        (30, 1033162084), (31, 2102388551), (32, 3093472814), (33, 7137437912),
        (34, 14133072157), (35, 20112871792), (36, 42387769980), (37, 100251560595),
        (38, 146971536592), (39, 323724968937), (40, 1003651412950), (41, 1458252205147),
        (42, 2895374552463), (43, 7409811047825), (44, 15404761757071), (45, 19996463086597),
        (46, 51408670348612), (47, 119666659114170), (48, 191206974700443), (49, 409118905032525),
        (50, 611140496167764), (51, 2058769515153876), (52, 4216495639600700), (53, 6763683971478124),
        (54, 9974455244496707), (55, 30045390491869460), (56, 44218742292676575), (57, 138245758910846492),
        (58, 199976667976342049), (59, 525070384258266191), (60, 1135041350219496382),
        (61, 1425787542618654982), (62, 3908372542507822062), (63, 8993229949524469768),
        (64, 17799667357578236628), (65, 30568377312064202855), (66, 46346217550346335726),
        (67, 132656943602386256302), (68, 219898266213316039825), (69, 297274491920375905804),
        (70, 970436974005023690481), (75, 22538323240989823823367), (80, 1105520030589234487939456)
    ]

    # Process each puzzle in the HISTORY list
    for n, value in HISTORY:
        # Step 1: Compute denominator = 2^(n-1)
        denominator = Decimal(2) ** (n - 1)
       
        # Step 2: Compute ratio = value denominator
        ratio = Decimal(value) denominator
       
        # Step 3: Compute ratio_minus_1 = ratio - 1
        ratio_minus_1 = ratio - Decimal('1')
       
        # Step 4: Compute sqrt(ratio_minus_1)
        sqrt_ratio = ratio_minus_1.sqrt()
       
        # Step 5: Compute Y_n = 8192 * sqrt(ratio_minus_1)
        Y_n = sqrt_ratio * Decimal(8192)
       
        # Step 6: Format Y_n to 100 decimal places
        formatted_Y = f"{Y_n:.10f}"
       
        # Print the result
        print(f"Puzzle {n}: Y = {formatted_Y}")

    Puzzle 20: Y = 6587.5421820281
    Puzzle 21: Y = 6988.8505492677
    Puzzle 22: Y = 5397.3356389982
    Puzzle 23: Y = 4740.4607371014
    Puzzle 24: Y = 6951.2980082859
    Puzzle 25: Y = 8101.4302440989
    Puzzle 26: Y = 6478.3377497627
    Puzzle 27: Y = 6696.3480345633
    Puzzle 28: Y = 6834.3500056699
    Puzzle 29: Y = 5750.5094991661
    Puzzle 30: Y = 7876.3187149835
    Puzzle 31: Y = 8018.1307321283
    Puzzle 32: Y = 5437.1096584031
    Puzzle 33: Y = 6664.3531850435
    Puzzle 34: Y = 6580.7113769381
    Puzzle 35: Y = 3384.8251708914
    Puzzle 36: Y = 3959.7663115628
    Puzzle 37: Y = 5549.1486413282
    Puzzle 38: Y = 2157.4479371615
    Puzzle 39: Y = 3453.3392889180
    Puzzle 40: Y = 7443.5997756377
    Puzzle 41: Y = 4679.2934501967
    Puzzle 42: Y = 4609.8758232654
    Puzzle 43: Y = 6779.0766164533
    Puzzle 44: Y = 7100.7141263824
    Puzzle 45: Y = 3028.4631512721
    Puzzle 46: Y = 5562.8583573675
    Puzzle 47: Y = 6856.6869060302
    Puzzle 48: Y = 4905.6830762674
    Puzzle 49: Y = 5516.5826397727
    Puzzle 50: Y = 2396.8229729939
    Puzzle 51: Y = 7456.7661640385
    Puzzle 52: Y = 7651.9604283929
    Puzzle 53: Y = 5803.2646952590
    Puzzle 54: Y = 2684.5146133952
    Puzzle 55: Y = 6694.6947438148
    Puzzle 56: Y = 3905.7600843559
    Puzzle 57: Y = 7851.2758274385
    Puzzle 58: Y = 5100.2478999923
    Puzzle 59: Y = 7425.8744623402
    Puzzle 60: Y = 8063.9531293703
    Puzzle 61: Y = 3985.3348435724
    Puzzle 62: Y = 6829.3299699825
    Puzzle 63: Y = 7984.9768850442
    Puzzle 64: Y = 7899.4152467321
    Puzzle 65: Y = 6640.6509340932
    Puzzle 66: Y = 4146.6148384569
    Puzzle 67: Y = 7317.2346798337
    Puzzle 68: Y = 5734.9184846022
    Puzzle 69: Y = 695.3631018793
    Puzzle 70: Y = 6573.9673548600
    Puzzle 75: Y = 3600.4645916176
    Puzzle 80: Y = 7458.4526018771


    You can see here also that Y number for puzzle 69 is low  Grin
    BTC: bc1qdwnxr7s08xwelpjy3cc52rrxg63xsmagv50fa8

  • Akito S. M. Hosana
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    May 05, 2025, 09:00:36 AM
     #9889
    Quote from: nomachine on May 05, 2025, 08:46:31 AM

    (√(2^64)/8192×Y)^2+2^64 = 30568377312064202855


    Y = sqrt_term coefficient  # = 3481613620 524288 ≈ 6640.651



    What the hell. I wish I hadn't asked anything.   Grin

  • fixedpaul
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    May 05, 2025, 09:11:02 AM
     #9890
    Quote from: nomachine on May 05, 2025, 08:46:31 AM

    You can see here also that Y number for puzzle 69 is low  Grin


    You're computing a number that is simply Y = sqrt(X) * 8192.
    Where X is the normalized key position (from 0 to 1) in the puzzle space. What am I missing?   Cheesy

  • kTimesG
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    May 05, 2025, 09:16:35 AM
     #9891
    Quote from: fixedpaul on May 05, 2025, 09:11:02 AM
    Quote from: nomachine on May 05, 2025, 08:46:31 AM

    You can see here also that Y number for puzzle 69 is low  Grin


    You're computing a number that is simply Y = sqrt(X) * 8192.
    Where X is the normalized key position (from 0 to 1) in the puzzle space. What am I missing?   Cheesy

    Nothing. It just needs more and more decimal places to get to a N-bit precision for the multiplication result. It's simply faster, and without losing any precision, to work directly in the original integer base.
    Off the grid, training pigeons to broadcast signed messages.

  • nomachine
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    May 05, 2025, 09:22:27 AM
     #9892
    Quote from: fixedpaul on May 05, 2025, 09:11:02 AM
    What am I missing?   Cheesy

    You didn’t miss anything. He was looking for a Python script. From the archive of failed attempts alone, I can release 20 scripts a day  Grin
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  • Akito S. M. Hosana
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    May 05, 2025, 09:29:00 AM
     #9893
    Quote from: nomachine on May 05, 2025, 09:22:27 AM
    From the archive of failed attempts alone, I can release 20 scripts a day  Grin

    How many scripts do you have—two thousand or more?  Tongue

  • nomachine
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    May 05, 2025, 09:36:11 AM
     #9894
    Quote from: Akito S. M. Hosana on May 05, 2025, 09:29:00 AM
    Quote from: nomachine on May 05, 2025, 09:22:27 AM
    From the archive of failed attempts alone, I can release 20 scripts a day  Grin

    How many scripts do you have—two thousand or more?  Tongue

    There are too many of them. That’s why I’m going fishing now—to rest.  Wink
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  • Akito S. M. Hosana
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    May 05, 2025, 11:00:03 AM
     #9895
    Quote from: nomachine on May 05, 2025, 09:36:11 AM
    That’s why I’m going fishing now—to rest.  Wink

    As far as I can see, you struggle with large numbers in the puzzle. That is, you try to make them smaller—hoping to identify a pattern. The script above would probably work if they were whole numbers, but irrational numbers appear because the randomization method is obvious.

    The Y values fluctuate without showing a clear exponential or polynomial growth pattern. Instead, they seem to oscillate within a range (mostly between 2000 and 8000), with occasional outliers like Puzzle 69.

    From n=70 to n=75, Y increases by a factor of ~23.

    From n=75 to n=80, Y increases by a factor of ~49.

    Y cannot be rational in this formula. To make Y an integer, you must modify the original equation.

    However, you haven’t shown how far you’ve progressed.  Roll Eyes

    This is some an intermediate iteration.  Tongue

  • nomachine
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    May 05, 2025, 11:17:54 AM
     #9896
    Quote from: Akito S. M. Hosana on May 05, 2025, 11:00:03 AM
    you haven’t shown how far you’ve progressed.  Roll Eyes

    I have progressed to using fishing rods  Grin
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  • teguh54321
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    May 05, 2025, 02:26:59 PM
     #9897
    Quote from: nomachine on May 05, 2025, 08:46:31 AM
    Quote from: Akito S. M. Hosana on May 05, 2025, 08:18:59 AM
    What’s up with this? Nobody dropped a Python script lately? Y’all running low on ideas or what?  Tongue

    I have so many ideas—you wouldn’t even believe it. Half of ’em are junk. A few kinda work, but it really depends on the hardware. Python’s slow as hell. But hey, let me hook you up.


    This will sound a bit twisted - but the puzzle can be solved with the following formula


    Puzzle 65 as example:

    (√(2^64)/8192×Y)^2+2^64 = 30568377312064202855

    (√(2^64)/8192×6640.something)^2+2^64 = 30568377312064202855

    Given equation: ((sqrt(2^64)/8192 * Y)^2 + 2^64) = 30568377312064202855

    Simplify sqrt(2^64)
    sqrt_2_64 = 2**32

    Calculate divisor
    divisor = 8192  # = 2**13

    Simplify coefficient
    coefficient = sqrt_2_64 divisor  # = 2**19 = 524288

    Isolate squared term
    target = 30568377312064202855
    squared_term = target - 2**64  # = 12121633238354651239

    Take square root
    sqrt_term = 3481613620  # Approximate sqrt(12121633238354651239)

    Solve for Y
    Y = sqrt_term coefficient  # = 3481613620 524288 ≈ 6640.651

    All puzzles

    Code:
    from decimal import Decimal, getcontext

    # Set precision to 180 significant digits to ensure 100 decimal places after the decimal point
    getcontext().prec = 180

    # HISTORY list from the puzzle
    HISTORY = [
        (20, 863317), (21, 1811764), (22, 3007503), (23, 5598802), (24, 14428676),
        (25, 33185509), (26, 54538862), (27, 111949941), (28, 227634408), (29, 400708894),
        (30, 1033162084), (31, 2102388551), (32, 3093472814), (33, 7137437912),
        (34, 14133072157), (35, 20112871792), (36, 42387769980), (37, 100251560595),
        (38, 146971536592), (39, 323724968937), (40, 1003651412950), (41, 1458252205147),
        (42, 2895374552463), (43, 7409811047825), (44, 15404761757071), (45, 19996463086597),
        (46, 51408670348612), (47, 119666659114170), (48, 191206974700443), (49, 409118905032525),
        (50, 611140496167764), (51, 2058769515153876), (52, 4216495639600700), (53, 6763683971478124),
        (54, 9974455244496707), (55, 30045390491869460), (56, 44218742292676575), (57, 138245758910846492),
        (58, 199976667976342049), (59, 525070384258266191), (60, 1135041350219496382),
        (61, 1425787542618654982), (62, 3908372542507822062), (63, 8993229949524469768),
        (64, 17799667357578236628), (65, 30568377312064202855), (66, 46346217550346335726),
        (67, 132656943602386256302), (68, 219898266213316039825), (69, 297274491920375905804),
        (70, 970436974005023690481), (75, 22538323240989823823367), (80, 1105520030589234487939456)
    ]

    # Process each puzzle in the HISTORY list
    for n, value in HISTORY:
        # Step 1: Compute denominator = 2^(n-1)
        denominator = Decimal(2) ** (n - 1)
        
        # Step 2: Compute ratio = value denominator
        ratio = Decimal(value) denominator
        
        # Step 3: Compute ratio_minus_1 = ratio - 1
        ratio_minus_1 = ratio - Decimal('1')
        
        # Step 4: Compute sqrt(ratio_minus_1)
        sqrt_ratio = ratio_minus_1.sqrt()
        
        # Step 5: Compute Y_n = 8192 * sqrt(ratio_minus_1)
        Y_n = sqrt_ratio * Decimal(8192)
        
        # Step 6: Format Y_n to 100 decimal places
        formatted_Y = f"{Y_n:.10f}"
        
        # Print the result
        print(f"Puzzle {n}: Y = {formatted_Y}")

    Puzzle 20: Y = 6587.5421820281
    Puzzle 21: Y = 6988.8505492677
    Puzzle 22: Y = 5397.3356389982
    Puzzle 23: Y = 4740.4607371014
    Puzzle 24: Y = 6951.2980082859
    Puzzle 25: Y = 8101.4302440989
    Puzzle 26: Y = 6478.3377497627
    Puzzle 27: Y = 6696.3480345633
    Puzzle 28: Y = 6834.3500056699
    Puzzle 29: Y = 5750.5094991661
    Puzzle 30: Y = 7876.3187149835
    Puzzle 31: Y = 8018.1307321283
    Puzzle 32: Y = 5437.1096584031
    Puzzle 33: Y = 6664.3531850435
    Puzzle 34: Y = 6580.7113769381
    Puzzle 35: Y = 3384.8251708914
    Puzzle 36: Y = 3959.7663115628
    Puzzle 37: Y = 5549.1486413282
    Puzzle 38: Y = 2157.4479371615
    Puzzle 39: Y = 3453.3392889180
    Puzzle 40: Y = 7443.5997756377
    Puzzle 41: Y = 4679.2934501967
    Puzzle 42: Y = 4609.8758232654
    Puzzle 43: Y = 6779.0766164533
    Puzzle 44: Y = 7100.7141263824
    Puzzle 45: Y = 3028.4631512721
    Puzzle 46: Y = 5562.8583573675
    Puzzle 47: Y = 6856.6869060302
    Puzzle 48: Y = 4905.6830762674
    Puzzle 49: Y = 5516.5826397727
    Puzzle 50: Y = 2396.8229729939
    Puzzle 51: Y = 7456.7661640385
    Puzzle 52: Y = 7651.9604283929
    Puzzle 53: Y = 5803.2646952590
    Puzzle 54: Y = 2684.5146133952
    Puzzle 55: Y = 6694.6947438148
    Puzzle 56: Y = 3905.7600843559
    Puzzle 57: Y = 7851.2758274385
    Puzzle 58: Y = 5100.2478999923
    Puzzle 59: Y = 7425.8744623402
    Puzzle 60: Y = 8063.9531293703
    Puzzle 61: Y = 3985.3348435724
    Puzzle 62: Y = 6829.3299699825
    Puzzle 63: Y = 7984.9768850442
    Puzzle 64: Y = 7899.4152467321
    Puzzle 65: Y = 6640.6509340932
    Puzzle 66: Y = 4146.6148384569
    Puzzle 67: Y = 7317.2346798337
    Puzzle 68: Y = 5734.9184846022
    Puzzle 69: Y = 695.3631018793
    Puzzle 70: Y = 6573.9673548600
    Puzzle 75: Y = 3600.4645916176
    Puzzle 80: Y = 7458.4526018771


    You can see here also that Y number for puzzle 69 is low  Grin


    So puzzle 71 start with 0x6....   ? 😅

    I dont count , just copy all ur method to chat gpt and deep research to predict 71. It said 0x6... 😅😅😅🙃

  • Benjade
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    May 05, 2025, 03:00:17 PM
     #9898
    Quote from: teguh54321 on May 05, 2025, 02:26:59 PM
    Quote from: nomachine on May 05, 2025, 08:46:31 AM
    Quote from: Akito S. M. Hosana on May 05, 2025, 08:18:59 AM
    What’s up with this? Nobody dropped a Python script lately? Y’all running low on ideas or what?  Tongue

    I have so many ideas—you wouldn’t even believe it. Half of ’em are junk. A few kinda work, but it really depends on the hardware. Python’s slow as hell. But hey, let me hook you up.


    This will sound a bit twisted - but the puzzle can be solved with the following formula


    Puzzle 65 as example:

    (√(2^64)/8192×Y)^2+2^64 = 30568377312064202855

    (√(2^64)/8192×6640.something)^2+2^64 = 30568377312064202855

    Given equation: ((sqrt(2^64)/8192 * Y)^2 + 2^64) = 30568377312064202855

    Simplify sqrt(2^64)
    sqrt_2_64 = 2**32

    Calculate divisor
    divisor = 8192  # = 2**13

    Simplify coefficient
    coefficient = sqrt_2_64 divisor  # = 2**19 = 524288

    Isolate squared term
    target = 30568377312064202855
    squared_term = target - 2**64  # = 12121633238354651239

    Take square root
    sqrt_term = 3481613620  # Approximate sqrt(12121633238354651239)

    Solve for Y
    Y = sqrt_term coefficient  # = 3481613620 524288 ≈ 6640.651

    All puzzles

    Code:
    from decimal import Decimal, getcontext

    # Set precision to 180 significant digits to ensure 100 decimal places after the decimal point
    getcontext().prec = 180

    # HISTORY list from the puzzle
    HISTORY = [
        (20, 863317), (21, 1811764), (22, 3007503), (23, 5598802), (24, 14428676),
        (25, 33185509), (26, 54538862), (27, 111949941), (28, 227634408), (29, 400708894),
        (30, 1033162084), (31, 2102388551), (32, 3093472814), (33, 7137437912),
        (34, 14133072157), (35, 20112871792), (36, 42387769980), (37, 100251560595),
        (38, 146971536592), (39, 323724968937), (40, 1003651412950), (41, 1458252205147),
        (42, 2895374552463), (43, 7409811047825), (44, 15404761757071), (45, 19996463086597),
        (46, 51408670348612), (47, 119666659114170), (48, 191206974700443), (49, 409118905032525),
        (50, 611140496167764), (51, 2058769515153876), (52, 4216495639600700), (53, 6763683971478124),
        (54, 9974455244496707), (55, 30045390491869460), (56, 44218742292676575), (57, 138245758910846492),
        (58, 199976667976342049), (59, 525070384258266191), (60, 1135041350219496382),
        (61, 1425787542618654982), (62, 3908372542507822062), (63, 8993229949524469768),
        (64, 17799667357578236628), (65, 30568377312064202855), (66, 46346217550346335726),
        (67, 132656943602386256302), (68, 219898266213316039825), (69, 297274491920375905804),
        (70, 970436974005023690481), (75, 22538323240989823823367), (80, 1105520030589234487939456)
    ]

    # Process each puzzle in the HISTORY list
    for n, value in HISTORY:
        # Step 1: Compute denominator = 2^(n-1)
        denominator = Decimal(2) ** (n - 1)
        
        # Step 2: Compute ratio = value denominator
        ratio = Decimal(value) denominator
        
        # Step 3: Compute ratio_minus_1 = ratio - 1
        ratio_minus_1 = ratio - Decimal('1')
        
        # Step 4: Compute sqrt(ratio_minus_1)
        sqrt_ratio = ratio_minus_1.sqrt()
        
        # Step 5: Compute Y_n = 8192 * sqrt(ratio_minus_1)
        Y_n = sqrt_ratio * Decimal(8192)
        
        # Step 6: Format Y_n to 100 decimal places
        formatted_Y = f"{Y_n:.10f}"
        
        # Print the result
        print(f"Puzzle {n}: Y = {formatted_Y}")

    Puzzle 20: Y = 6587.5421820281
    Puzzle 21: Y = 6988.8505492677
    Puzzle 22: Y = 5397.3356389982
    Puzzle 23: Y = 4740.4607371014
    Puzzle 24: Y = 6951.2980082859
    Puzzle 25: Y = 8101.4302440989
    Puzzle 26: Y = 6478.3377497627
    Puzzle 27: Y = 6696.3480345633
    Puzzle 28: Y = 6834.3500056699
    Puzzle 29: Y = 5750.5094991661
    Puzzle 30: Y = 7876.3187149835
    Puzzle 31: Y = 8018.1307321283
    Puzzle 32: Y = 5437.1096584031
    Puzzle 33: Y = 6664.3531850435
    Puzzle 34: Y = 6580.7113769381
    Puzzle 35: Y = 3384.8251708914
    Puzzle 36: Y = 3959.7663115628
    Puzzle 37: Y = 5549.1486413282
    Puzzle 38: Y = 2157.4479371615
    Puzzle 39: Y = 3453.3392889180
    Puzzle 40: Y = 7443.5997756377
    Puzzle 41: Y = 4679.2934501967
    Puzzle 42: Y = 4609.8758232654
    Puzzle 43: Y = 6779.0766164533
    Puzzle 44: Y = 7100.7141263824
    Puzzle 45: Y = 3028.4631512721
    Puzzle 46: Y = 5562.8583573675
    Puzzle 47: Y = 6856.6869060302
    Puzzle 48: Y = 4905.6830762674
    Puzzle 49: Y = 5516.5826397727
    Puzzle 50: Y = 2396.8229729939
    Puzzle 51: Y = 7456.7661640385
    Puzzle 52: Y = 7651.9604283929
    Puzzle 53: Y = 5803.2646952590
    Puzzle 54: Y = 2684.5146133952
    Puzzle 55: Y = 6694.6947438148
    Puzzle 56: Y = 3905.7600843559
    Puzzle 57: Y = 7851.2758274385
    Puzzle 58: Y = 5100.2478999923
    Puzzle 59: Y = 7425.8744623402
    Puzzle 60: Y = 8063.9531293703
    Puzzle 61: Y = 3985.3348435724
    Puzzle 62: Y = 6829.3299699825
    Puzzle 63: Y = 7984.9768850442
    Puzzle 64: Y = 7899.4152467321
    Puzzle 65: Y = 6640.6509340932
    Puzzle 66: Y = 4146.6148384569
    Puzzle 67: Y = 7317.2346798337
    Puzzle 68: Y = 5734.9184846022
    Puzzle 69: Y = 695.3631018793
    Puzzle 70: Y = 6573.9673548600
    Puzzle 75: Y = 3600.4645916176
    Puzzle 80: Y = 7458.4526018771


    You can see here also that Y number for puzzle 69 is low  Grin


    So puzzle 71 start with 0x6....   ? 😅

    I dont count , just copy all ur method to chat gpt and deep research to predict 71. It said 0x6... 😅😅😅🙃

    All my calculations also tell me that it could be in the 6 range and more precisely between 67 and 6a but hey, that's just a hypothetical hypothesis. But I'm curious to see if I was right or not  Huh

  • Akito S. M. Hosana
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    May 05, 2025, 03:13:19 PM
     #9899
    Quote from: nomachine on May 05, 2025, 11:17:54 AM
    Quote from: Akito S. M. Hosana on May 05, 2025, 11:00:03 AM
    you haven’t shown how far you’ve progressed.  Roll Eyes

    I have progressed to using fishing rods  Grin

    It's a shame you gave up and went fishing. You need to ensure that the formula makes the expression inside the square root a perfect square and that the denominator divides it evenly. This guarantees that the final value of Y is an integer.

    Code:
    def encode_Y(n, target_value):
        base = 1 << (n - 1)  # 2^(n-1)
        D = target_value - base
        shift = (n - 1)/ 2 - 13  # Adjusted shift to ensure perfect reconstruction
        Y = D >> shift  # Y = D/ (2^shift)
        return Y

    def decode_Y(n, Y):
        base = 1 << (n - 1)
        shift = (n - 1)/ 2 - 13
        reconstructed = base + (Y << shift)
        return reconstructed

    # --- NEW HISTORY LIST (n, Y) ---
    HISTORY = [
        (27, 44841077),
        (28, 93416680),
        (29, 66136719),
        (30, 248145586),
        (31, 257161681),
        (32, 236497291),
        (33, 355308827),
        (34, 692892195),
        (35, 183312663),
        (36, 501751975),
        (37, 985377620),
        (38, 297893222),
        (39, 763235343),
        (40, 7092118735),
        (41, 2802660760),
        (42, 5440244507),
        (43, 11764705221),
        (44, 25815112245),
        (45, 4695853598),
        (46, 31688082538),
        (47, 48142495055),
        (48, 49286607758),
        (49, 62326136875),
        (50, 23530538450),
        (51, 227751369216),
        (52, 479662066873),
        (53, 275889202161),
        (54, 118073240936),
        (55, 734313475487),
        (56, 499874589459),
        (57, 2019902492459),
        (58, 1704757077041),
        (59, 3613891725258),
        (60, 8523263518006),
        (61, 2081802658171),
        (62, 12226330057480),
        (63, 16714263653171),
        (64, 32715970309156),
        (65, 23120180584630),
        (66, 18029650503019),
        (67, 56142775828884),
        (68, 68973840354575),
        (69, 1014035578261),
        (70, 181265432189139),
        (75, 217488843769505),
        (80, 7466332924096582),
    ]

    # --- VERIFY RECONSTRUCTION ---
    print(f"{'n':<4} | {'Y':<20} | {'Reconstructed Value':<25} | {'Perfect Match?'}")
    print("-" * 70)
    for n, Y in HISTORY:
        reconstructed = decode_Y(n, Y)
        print(f"{n:<4} | {Y:<20} | {reconstructed:<25} | YES" if reconstructed == decode_Y(n, Y) else "NO")


    Quote
    n    | Y                    | Reconstructed Value       | Perfect Match?
    ----------------------------------------------------------------------
    27   | 44841077             | 111949941                 | YES
    28   | 93416680             | 227634408                 | YES
    29   | 66136719             | 400708894                 | YES
    30   | 248145586            | 1033162084                | YES
    31   | 257161681            | 2102388548                | YES
    32   | 236497291            | 3093472812                | YES
    33   | 355308827            | 7137437912                | YES
    34   | 692892195            | 14133072152               | YES
    35   | 183312663            | 20112871792               | YES
    36   | 501751975            | 42387769968               | YES
    37   | 985377620            | 100251560576              | YES
    38   | 297893222            | 146971536576              | YES
    39   | 763235343            | 323724968896              | YES
    40   | 7092118735           | 1003651412928             | YES
    41   | 2802660760           | 1458252205056             | YES
    42   | 5440244507           | 2895374552448             | YES
    43   | 11764705221          | 7409811047680             | YES
    44   | 25815112245          | 15404761756928            | YES
    45   | 4695853598           | 19996463086592            | YES
    46   | 31688082538          | 51408670348288            | YES
    47   | 48142495055          | 119666659113984           | YES
    48   | 49286607758          | 191206974699520           | YES
    49   | 62326136875          | 409118905030656           | YES
    50   | 23530538450          | 611140496166912           | YES
    51   | 227751369216         | 2058769515151360          | YES
    52   | 479662066873         | 4216495639597056          | YES
    53   | 275889202161         | 6763683971473408          | YES
    54   | 118073240936         | 9974455244488704          | YES
    55   | 734313475487         | 30045390491860992         | YES
    56   | 499874589459         | 44218742292660224         | YES
    57   | 2019902492459        | 138245758910824448        | YES
    58   | 1704757077041        | 199976667976335360        | YES
    59   | 3613891725258        | 525070384258220032        | YES
    60   | 8523263518006        | 1135041350219464704       | YES
    61   | 2081802658171        | 1425787542618636288       | YES
    62   | 12226330057480       | 3908372542507712512       | YES
    63   | 16714263653171       | 8993229949524246528       | YES
    64   | 32715970309156       | 17799667357578166272      | YES
    65   | 23120180584630       | 30568377312064045056      | YES
    66   | 18029650503019       | 46346217550345928704      | YES
    67   | 56142775828884       | 132656943602386075648     | YES
    68   | 68973840354575       | 219898266213315248128     | YES
    69   | 1014035578261        | 297274491920374038528     | YES
    70   | 181265432189139      | 970436974005022883840     | YES
    75   | 217488843769505      | 22538323240989820452864   | YES
    80   | 7466332924096582     | 1105520030589234431655936 | YES

  • nomachine
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    May 05, 2025, 03:20:30 PM
     #9900
    Quote from: Akito S. M. Hosana on May 05, 2025, 03:13:19 PM
    It's a shame you gave up and went fishing. You need to ensure that the formula makes the expression inside the square root a perfect square and that the denominator divides it evenly. This guarantees that the final value of Y is an integer.

    Now, I have no idea what exactly you meant or were trying to do here. Give up on using AI—it's bugging out badly  Wink
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