Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Brain Teaser #84

  1. Apr 17, 2004 #1
    It's time to study ancient Laurasian civilization. Here's an important formula that may or may not look familiar:

    L = J'6oAL EL5J YCAQ JC5C 68oL -> 5'TYoA QELL |6T5 LLC5 J5dd i

    Some common numerical sequences are encoded below:

    J, d, E, o, Q, LL, Ld, L8, dQ, E2, 56, o8, J|2, JE8, T88, Y26, YA2, P2L, U2Q

    L, h, 5, LY, oY, hQ|, Ld6|, 2QY|, EY2Y|, do EBV, h5L LEV, L9Y9 B9V, L odhY 99V

    L, L, h, d, [, Y, Q, L[, hh, do, [2, 2/, e2, Lo2, hJh, dQ6, JdQ, SLY, L/[[, LSJQ

    /, b, J, S, B, /Z, /9, h7, hQ, bo, 7h, 7e, Z6, J2, oY, YY, 22, S6, 6e, Qh, eo, BQ

    /, 7, 2, //, /2, h7, 6/, 7/, Z/, J7, oY, 2/, S2, 97, e/, /V, /h/, /77, /J2, /2/

    But something was lost in the transliteration. To make this scheme consistent, what diacritical mark should be added to the o?

    Hint: The arrow is exponentiation.
     
    Last edited: Apr 17, 2004
  2. jcsd
  3. Apr 17, 2004 #2
    dear god!!!!!
     
  4. Apr 17, 2004 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    come on padraig it is not that bad
    the imaginary number i is carried over unchanged
    and the first line says 1 = e raised to power 2 pi i
    e is 2.71828... worked out in base 16 I suppose
    pi is 6.283185... again I would guess in base 16 because

    they are using base 16
    and L = 1
    h = 2
    d = 3
    [ = 5


    I rather suspect that the third sequence is the Fibonacci numbers
    1,1,2,3,5,8,13, 21,.....

    so that would make Y = 8
    and Q = 13
    and L[ would be 1 in the 16s place and 5 in the ones place, or 21
    so it works out
     
    Last edited: Apr 17, 2004
  5. Apr 17, 2004 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    I have used the edit to correct a mistake that davilla mentioned.
    the euler formula 1 = e2πi
    and the fibonacci numbers

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,

    putting that in 16-base (hexadecimal) gives

    1, 1, 2, 3, 5, 8, "13", 15, 22, 37, 59, 90, "14"9, 179, 262

    this shows that the slash / must be the zero in the notation

    / = 0
    L = 1
    h = 2
    d = 3

    [ = 5
    J = 6
    o = 7
    Y = 8
    2 = 9

    Q = 13
    e = 14
     
    Last edited: Apr 23, 2004
  6. Apr 17, 2004 #5

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    L = J'6oAL EL5J YCAQ JC5C 68oL -> 5'TYoA QELL |6T5 LLC5 J5dd i

    L, L, h, d, [, Y, Q, L[, hh, do, [2, 2/, e2, Lo2, hJh, dQ6, JdQ, SLY, L/[[, LSJQ

    the euler formula 1 = e2πi
    and the fibonacci numbers

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,

    putting that in 16-base (hexadecimal) gives

    1, 1, 2, 3, 5, 8, D = "13", 15, 22, 37, 59, 90, "14"9, 179, 262, 3 "13" "11", 63 "13", "10" 18, 1055, 1 "10" 6 "13"

    this shows that the slash / must be the zero in the notation

    / = 0
    L = 1
    h = 2
    d = 3
    ....
    [ = 5
    J = 6
    o = 7
    Y = 8
    2 = 9
    S = 10
    6 = 11
    Q = 13
    e = 14
     
    Last edited: Apr 23, 2004
  7. Apr 17, 2004 #6

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    there may be inconsistent stuff mixed in
    but that is a start on it
    at least one sequence is the fibonacci
    in base-16

    somebody else see if they can take it further
     
  8. Apr 17, 2004 #7

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    L = J'6oAL EL5J YCAQ JC5C 68oL -> 5'TYoA QELL |6T5 LLC5 J5dd i

    L, L, h, d, [, Y, Q, L[, hh, do, [2, 2/, e2, Lo2, hJh, dQ6, JdQ, SLY, L/[[, LSJQ

    the euler formula 1 = e2πi
    and the fibonacci numbers

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,

    putting that in 16-base (hexadecimal) gives

    1, 1, 2, 3, 5, 8, D = "13", 15, 22, 37, 59, 90, "14"9, 179, 262, 3 "13" "11", 63 "13", "10" 18, 1055, 1 "10" 6 "13"


    / = 0
    L = 1
    h = 2
    d = 3
    7 = 4
    [ = 5
    J = 6
    o = 7
    Y = 8
    2 = 9
    S = 10
    6 = 11
    9 = 12
    Q = 13
    e = 14
    B = 15

    the last sequence is the sequence of squares, 1, 4, 9, 16, 25, 36,...
    but written in hexadecimal and with some alternative numerals
    the three, which was d, can be turned front to back and appear as 6
    the four can also be written 7

    here is the sequence of squares:
    L, 7, 2, L/, L2, h7, dL, 7/, [L, J7, o2, 2/, S2, 97, eL, L//, LhL, L77, LJ2, L2/

    here is how this transliterates to hex
    1, 4, 9, 10, 19, 24, 31, 40, 51, 64, 79, 90, "ten"9, "twelve"4, "14"1, 100, 121....

    here is how this converts to decimal

    1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, ...
     
    Last edited: Apr 23, 2004
  9. Apr 17, 2004 #8

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Translations of three of the 5 sequences

    L, L, h, d, [, Y, Q, L[, hh, do, [2, 2/, e2, Lo2, hJh, dQ6, JdQ, SLY, L/[[, LSJQ

    Fibonacci: 1, 1, 2, 3, ....

    L, b, J, S, B, LZ, L9, h7, hQ, bo, 7h, 7e, Z6, J2, oY, YY, 22, S6, 6e, Qh, eo, BQ

    bowling pin numbers, triangular numbers:
    1, 3, 6, 10, 15, 21,...

    L, 7, 2, L /, L2, h7, 6L, 7/, ZL, J7, oY, 2/, S2, 97, eL, L//, LhL, L77, LJ2, L2/

    the squares:
    1, 4, 9, 16, 25,...
     
    Last edited: Apr 17, 2004
  10. Apr 18, 2004 #9
    Wow, lots of progress. There is one error in your table, but you are right on everything else. So, can anyone solve the puzzle?


    Incidentally, the Mayans used a base 20 number system with symbols using bars and dots. The dot is one and the bar is five, so the largest digit was written with four dots on top of three bars. Does anyone know of other civilizations using a base other than 10? Even the Romans grouped by 10.
     
    Last edited: Apr 19, 2004
  11. Apr 18, 2004 #10
    I remember when brain teasers were written in english.
     
  12. Apr 18, 2004 #11
    :biggrin: :biggrin: :biggrin: :biggrin:
     
  13. Apr 18, 2004 #12
    English has my vote.
     
  14. Apr 19, 2004 #13
    Brain teasers?!? These are just cruel!
     
  15. Apr 19, 2004 #14
    Sorry, I didn't intend any permanent damage to your eyes. It looks really complicated only because there's more information provided than is needed. The values used for e and pi were precise to 24 decimals, but that formula can be completely ignored if desired.

    With a working interpretation, the toughest number chunching has already been done, although the work has gone unverified. That doesn't mean the answer is immediate, but it does require some human thinking in contrast to the more boring stuff a supercomputer can do.

    If catching the lingering mistake isn't enough to solve the problem, there are extra clues in symbols that have not been identified. Marcus even mentioned that the d can be flipped front to back, a fact that he omitted from the table.
     
    Last edited: Apr 22, 2004
  16. Apr 21, 2004 #15
    Second Hint:

    Confused by apparent contradictions in their decoding scheme, anthropologists went back to the site to discover that the J in the most recent carvings, including the formula, was written with one stroke, whereas the J that they had determined to represent six was written with two.
     
    Last edited: Apr 25, 2004
  17. Apr 22, 2004 #16

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    hi davilla, that's a fascinating puzzle and I am surprised that no one else has stepped in and furthered the progress already made on it

    basically I would like to share the fun
    and not be the only person responding

    when other people dont try it suggest to me that they arent interested
    so I dont want to just talk to myself

    if other people chip in and help then I will get back to it too
    because I can see that I have a mistake in either 4 or 7 and
    that there are more things to discover about the way they have
    of writing numerals

    like zero is /
    and one is / with an underline, which looks like L or else like /

    so maybe this is a Laurasian rule that the next number is made by putting
    an underline

    stuff like that

    and I have a guess as to which sequence involves prime numbers

    but if no one else tries to answer then I should not just be talking to a blank wall

    anyway, brava and kudos for the puzzlemaking
     
  18. Apr 22, 2004 #17
    I have no idea. I've been pondering. My guess is an anunaasika, but that's purely a guess.

    The only thing I can think of is that the e is a small c with a diacritic bar through it.

    Hey, I've gave it all I got, to no avail. Good luck.

    Paden Roder
     
  19. Apr 22, 2004 #18
    Hmm... sorry I didn't even notice this one until now. And I can't work on it now. Davilla mentioned on the first page something about other number systems, but it's not clear whether that was a hint or just a point of general interest. So I'll just remind everyone that the Babylonians and Sumerians used a sexagesimal (base 60) number system in case it might be relevant to solving the rest of this puzzle.
     
  20. Apr 23, 2004 #19

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    I think the problem is solved---at least in this sense: we know that the last 3 sequences are Fibs, triangular numbers, and squares.
    We know the system is hexadecimal with these symbols:


    / = 0
    L = 1
    h = 2
    d = 3
    7 = 4
    [ = 5
    J = 6
    o = 7
    Y = 8
    2 = 9
    S = 10
    6 = 11
    9 = 12
    Q = 13
    e = 14
    B = 15

    That constitutes a complete decoding, as far as I can see. A mistake mentioned by davilla has been corrected.

    However there is still the formula to check, plus these two sequences

    J, d, E, o, Q, LL, Ld, L8, dQ, E2, 56, o8, J|2, JE8, T88, Y26, YA2, P2L, U2Q

    L, h, 5, LY, oY, hQ|, Ld6|, 2QY|, EY2Y|, do EBV, h5L LEV, L9Y9 B9V, L odhY 99V

    The J in the first sequence may just be a typo. It should probably be h (to stand for 2, the first prime number). My concern about this is that
    if the rest turn out to be consistent then nothing new is learned
    and if they turn out to be inconsistent then its a mess. because we already have a complete decoding.

    Like suppose these Laurasians thought that they were writing the prime numbers, but they left out some? then the first sequence is going to screw us up!

    in any culture, the primes are:
    2,3,5,7,11,13,17,19,23, 29, 31, 37, ...

    when I look at the first Laurasian sequence I dont see "11" which they write 6.

    h, d, [, o, (6, for 11, is missing) Q, LL, Ld, (Lo, for 23, missing) (LQ, for 29, missing) LB,...

    so there are a lot of primes in their sequence but not all----there are gaps
     
  21. Apr 24, 2004 #20
    Some additions to marcus' decoding:

    / and | = 0
    L and /_ = 1
    h and J = 2
    d, T, b and | = 3
    7, 6 and T = 4
    [, Z and E = 5
    J and 5 = 6
    o and 8 = 7
    Y = 8
    2 = 9
    S = 10
    6 = 11
    9 = 12
    Q = 13
    A and e = 14
    B = 15

    Of course, some of these apparent dual meanings may simply be typos or arithmetic errors on the part of the Laurasians.

    As for the primes, I guess they left out some figuring we didn't need all of them. On the other hand, they included o8=77h=119d which doesn't belong there (unless 8 sometimes means 1 or 15).

    The second sequence is factorials, except they listed LY=18h=26d instead of 24d (unless Y sometimes means 6).

    The J is not a typo, that's the dual meaning that davilla mentioned (turns out to be just one of many dual meanings). In the formula, and the prime sequence J has to be 2; in the fibonacci and prime sequences, it is 6.

    So now I think everything is decoded except the underlying basis for the code scheme itself, which, if someone finds it, will presumably lead to the solution.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Brain Teaser #84
  1. Brain Teaser #19 (Replies: 4)

  2. President Brain teaser (Replies: 12)

  3. Brain teaser question (Replies: 10)

Loading...