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Math Help - 196 - algorithm ? Why is everyone saying there is no answer?

  1. #1
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    196 - algorithm ? Why is everyone saying there is no answer?

    edit: Case Closed, There was an error in my actionscript that produced the wrong numbers for adding when the numbers contain leading zeros. (see in posts below)

    I recently read up on this whole 196 algorithm thing about palindrome numbers... I am very confused. People say that there have been programs built to calculate out this sequence and that no one has been able to find a palindrome that this number produces when applied to the algorithm... Being the person I am, I went out and wrote a quick program in acitonscript.. Within about 0.8 seconds it returned a result... I don't understand, am I doing it wrong or something? Why is everyone saying it has been calculated out to millions of digits with no result when my computer is showing a result after only a few results???

    Here is what my code returned:


    196 + 691 = 887
    887 + 788 = 1675
    1675 + 5761 = 7436
    7436 + 6347 = 13783
    13783 + 38731 = 52514
    52514 + 41525 = 94039
    94039 + 93049 = 187088
    187088 + 880781 = 1067869
    1067869 + 9687601 = 10755470
    10755470 + 07455701 = 12745039
    12745039 + 93054721 = 105799760
    105799760 + 067997501 = 173797261
    173797261 + 162797371 = 336594632
    336594632 + 236495633 = 573090265
    573090265 + 562090375 = 1135180640
    1135180640 + 0460815311 = 1595995951


    As you can see the final result is a palindrome?

    What am I doing wrong?
    Last edited by orange gold; January 14th 2011 at 04:01 AM.
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  2. #2
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    Quote Originally Posted by orange gold View Post
    I recently read up on this whole 196 algorithm thing about palindrome numbers... I am very confused. People say that there have been programs built to calculate out this sequence and that no one has been able to find a palindrome that this number produces when applied to the algorithm... Being the person I am, I went out and wrote a quick program in acitonscript.. Within about 0.8 seconds it returned a result... I don't understand, am I doing it wrong or something? Why is everyone saying it has been calculated out to millions of digits with no result when my computer is showing a result after only a few results???

    Here is what my code returned:


    196 + 691 = 887
    887 + 788 = 1675
    1675 + 5761 = 7436
    7436 + 6347 = 13783
    13783 + 38731 = 52514
    52514 + 41525 = 94039
    94039 + 93049 = 187088
    187088 + 880781 = 1067869
    1067869 + 9687601 = 10755470
    10755470 + 07455701 = 12745039
    12745039 + 93054721 = 105799760
    105799760 + 067997501 = 173797261
    173797261 + 162797371 = 336594632
    336594632 + 236495633 = 573090265
    573090265 + 562090375 = 1135180640
    1135180640 + 0460815311 = 1595995951


    As you can see the final result is a palindrome?

    What am I doing wrong?

    I think that it may be that you're confusing what the 196 alg. states: if you take any number and add it to its reverse, take the result and add it to its reverse, etc., at some point you'll get a palindrome number, and this is precisely what you got!

    Tonio
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  3. #3
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    10755470 + 07455701 = 12745039
    This line is wrong.
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  4. #4
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    Ahh! I know, but the theory also lists a few numbers that have been found to not have a palindrome appear. Even after millions of reverse-then-add algorithms. The list goes: 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, 1765, 1767, 1855, 1857, 1945, 1947, 1997, etc.
    People have claimed to have made programs to calculate the numbers 196 produces out to results with millions of digits and still have a palindrome not produce??? This is the whole reason it was named the 196-algorithm.
    However I can't see how they can't find a palindrome for 196? It seems to 16th result.

    Lychrel number - Wikipedia, the free encyclopedia
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  5. #5
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    Quote Originally Posted by emakarov View Post
    This line is wrong.
    Thankyou! I wonder what is wrong with my code to produce such a weird thing?
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  6. #6
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    Quote Originally Posted by orange gold View Post
    I recently read up on this whole 196 algorithm thing about palindrome numbers... I am very confused. People say that there have been programs built to calculate out this sequence and that no one has been able to find a palindrome that this number produces when applied to the algorithm... Being the person I am, I went out and wrote a quick program in acitonscript.. Within about 0.8 seconds it returned a result... I don't understand, am I doing it wrong or something? Why is everyone saying it has been calculated out to millions of digits with no result when my computer is showing a result after only a few results???

    Here is what my code returned:


    196 + 691 = 887
    887 + 788 = 1675
    1675 + 5761 = 7436
    7436 + 6347 = 13783
    13783 + 38731 = 52514
    52514 + 41525 = 94039
    94039 + 93049 = 187088
    187088 + 880781 = 1067869
    1067869 + 9687601 = 10755470
    10755470 + 07455701 = 12745039
    12745039 + 93054721 = 105799760
    105799760 + 067997501 = 173797261
    173797261 + 162797371 = 336594632
    336594632 + 236495633 = 573090265
    573090265 + 562090375 = 1135180640
    1135180640 + 0460815311 = 1595995951


    As you can see the final result is a palindrome?

    What am I doing wrong?
    Oh, I think I know what you meant (though not what you wrote): you meant that 196 is a Lichrel nu7mber, meaning hat applying to it the 196 alg. you won't get a palindrome ever (this hasn't been proved, though)

    Well, you've a mistake in line 10 in your calculations.

    Tonio
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  7. #7
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    AHH! I can't fix the problem ahah, Well I assume that it is a lichrel number, I tried to fix the code but it didn't work, I eventually just started the program with the correct number from line 10 and the program terminated because the numbers got to big.

    I still don't know why the code doesn't work starting with 196, here it is if anyone is curious:
    Actionscript 2.0:
    Code:
    num = 196;
    _root.onEnterFrame = function() {
    	numberText.text = num
    	rvsString = "";
        for (i=numberText.text.length; i>=0; i=i-1) {
            rvsString += numberText.text.charAt(i);
        }
        num2 = rvsString;
    	if (num != num2) {
    		num3 = num-(-num2); //subtract a negative becuase using the + operator causes the adding of strings... ex. 54 + 31 = 5431  ||*||  but  ||*|| 54 - (-31) = 85
    		trace(num + " + " + num2 + " = " + num3);
    		num = num-(-num2);
    	}
    }
    Where "numberText" is the name of a dynamic text-field in the .fla file.
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  8. #8
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    Must be an error with the way acitonscript interprets addition problems with leading zeros ..

    Ex. This code:
    Code:
    num1 = 0000000000000010755470 + 7455701
    num2 = 010755470 + 7455701
    num3 = 10755470 + 000000000000007455701
    num4 = 10755470 + 07455701
    num5 = 0000000000000010755470 + 000000000000007455701
    num6 = 010755470 + 07455701
    num7 = 10755470 + 7455701
    trace(num1)
    trace(num2)
    trace(num3)
    trace(num4)
    trace(num5)
    trace(num6)
    trace(num7)
    produces this result:

    9805581
    9805581
    12745039
    12745039
    4339449
    4339449
    18211171




    They should all be equal... Anyways, case closed. Thanks forum!
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  9. #9
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    Numbers starting with 0 are interpreted as octal. So, 7455701_8=1989569_{10}, and 10755470 + 1989569 = 12745039, which is what your program produced.
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