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Parallel processing test: Mental arithmetic

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I'm in doubt whether my tulpas can think while I'm concentrating on something other than them, so I figured I need some test that keeps them occupied reliably for some time while I explicitly concentrate on something else, and that produces a measurable result.


I came up with a test based on mental arithmetic. The idea is to perform a very long series of arithmetic operations, with little apparent repetitive structure, so the tulpa cannot jump ahead to the result after recognizing the pattern behind these calculations, but instead needs to go through all calculations manually. No cooperation from the host side required if everything goes well.


The test (sequence A)


During the test, the tulpa produces a sequence of numbers, generated by the following rule: The first number is 23. The next number is always obtained by adding the tens digit of the previous number, plus six times the unit digit.


So the first numbers in the sequence are:

  1. 23
  2. 2 + 6 * 3 = 20
  3. 2 + 6 * 0 = 02
  4. 0 + 6 * 2 = 12

You don't have to memorize the whole sequence. We just want to test whether you (the tulpa) worked your way through the whole sequence, so all you have to remember is something like "the 3rd number is 2", then later "the 4th number is 12" and so on.


Before you start, tell your host how much time you plan to spend computing. After the set time, have your host ask you for your progress. For example, you would say "the 69th number is 08". The host then checks your result with this lookup table that has the first 1000 elements of the sequence.


The test (sequence B)


If two-digit arithmetic is too easy, here's another sequence: Start at 273, and obtain the next number in the sequence by doubling the previous number, removing the thousands digit if one occurs, and subtracting one.


For example, suppose the first number in the sequence is 273: Double this (546); remove thousands digit (none, so still 546); minus one gives 545. This is the second number. Now, double this (1090); remove thousands digit (90); minus one gives 89. This is the third number.


Here's the lookup table, again for the first 1000 elements.


Call for participation


From preliminary checks, it seems like I need to work with my tulpas on their mental arithmetic first before we can actually take this test. Nonetheless, this post being in the research board means that you're all welcome to partake in it.


Tulpas, please note that the seemingly random structure of the sequences mean that a tiny error anywhere inbetween can completely throw you off. So if you want to be succesful, be sure to double-check and triple-check each step.


My original intention is to get a positive result at all from my tulpas, but of course you can easily turn this into a challenge in multiple ways, e.g. try to compute the 50th element as fast as possible. Have fun!

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