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Posts posted by Pickett

  1. 1 hour ago, jasen said:

    Some of your solutions is wrong, "adjacent" also means adjacent diagonally. Re filter your answers.

    Reflection works vertically

    Ah, I missed a few of the diagonals (I accounted for the center square but not all):


    2 unique solutions, 1 reflection per solution (across the X-Axis)

    A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13    
    A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7       (G+H+I) = (A+B+C) =13    

    A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3       (G+H+I) = (A+B+C) =17    
    A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17 


  2. Spoiler

    So reflections/rotations get a little strange with this because of the fact that you have stated that the middle-left and middle-middle squares can be a difference of 1. This means if you have a solution that works...and then reflect it across the Y-axis, there's a possibility that that reflected solution is not a valid solution anymore. Here's an example of this:

    This solution works with the original configuration:

    A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13  

    If I reflect that across the Y-axis...you get this (which is no longer valid because E/F have a difference one 1):

    A=7, B=5, C=1, D=2, E=9, F=8, G=4, H=6, I=3       (G+H+I) = (A+B+C) =13

    With that being said, I could spend the time figuring out which ones are the true reflections/rotations/duplicates (some are easy to figure out) and which ones aren't...but here's all 24 of the possible solutions to the above:

    A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13    
    A=1, B=7, C=3, D=8, E=9, F=6, G=5, H=2, I=4       (G+H+I) = (A+B+C) =11    
    A=1, B=7, C=5, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13    
    A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7       (G+H+I) = (A+B+C) =13    
    A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=7, I=5       (G+H+I) = (A+B+C) =13    
    A=3, B=6, C=4, D=8, E=9, F=2, G=5, H=1, I=7       (G+H+I) = (A+B+C) =13    
    A=3, B=7, C=1, D=8, E=9, F=6, G=5, H=2, I=4       (G+H+I) = (A+B+C) =11    
    A=3, B=7, C=2, D=8, E=9, F=4, G=5, H=1, I=6       (G+H+I) = (A+B+C) =12    
    A=5, B=1, C=6, D=8, E=9, F=4, G=3, H=7, I=2       (G+H+I) = (A+B+C) =12    
    A=5, B=1, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13    
    A=5, B=2, C=4, D=8, E=9, F=6, G=1, H=7, I=3       (G+H+I) = (A+B+C) =11    
    A=5, B=2, C=4, D=8, E=9, F=6, G=3, H=7, I=1       (G+H+I) = (A+B+C) =11    
    A=5, B=8, C=6, D=2, E=1, F=4, G=7, H=3, I=9       (G+H+I) = (A+B+C) =19    
    A=5, B=8, C=6, D=2, E=1, F=4, G=9, H=3, I=7       (G+H+I) = (A+B+C) =19    
    A=5, B=9, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17    
    A=5, B=9, C=4, D=2, E=1, F=6, G=7, H=3, I=8       (G+H+I) = (A+B+C) =18    
    A=7, B=3, C=8, D=2, E=1, F=6, G=5, H=9, I=4       (G+H+I) = (A+B+C) =18    
    A=7, B=3, C=9, D=2, E=1, F=4, G=5, H=8, I=6       (G+H+I) = (A+B+C) =19    
    A=7, B=4, C=6, D=2, E=1, F=8, G=5, H=9, I=3       (G+H+I) = (A+B+C) =17    
    A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=3, I=5       (G+H+I) = (A+B+C) =17    
    A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3       (G+H+I) = (A+B+C) =17    
    A=9, B=3, C=5, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17    
    A=9, B=3, C=7, D=2, E=1, F=4, G=5, H=8, I=6       (G+H+I) = (A+B+C) =19    
    A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17    


  3. Spoiler

    Not accounting for rotations, there are 48 solutions to this problem.

    If you account for the fact that this can be rotated 6 times, I see 8 unique solutions.

    Below are the 8 unique solutions (with each of the 5 other equal rotations shown)...

    Solution 1:    A=1, B=2, C=9, D=11, E=6, F=10, G=14, H=4, I=8, J=3, K=5, L=12, M=13
        A=13, B=12, C=5, D=3, E=8, F=4, G=14, H=10, I=6, J=11, K=9, L=2, M=1
        A=2, B=8, C=10, D=9, E=1, F=3, G=14, H=11, I=13, J=5, K=4, L=6, M=12
        A=12, B=6, C=4, D=5, E=13, F=11, G=14, H=3, I=1, J=9, K=10, L=8, M=2
        A=8, B=13, C=3, D=10, E=2, F=5, G=14, H=9, I=12, J=4, K=11, L=1, M=6
        A=6, B=1, C=11, D=4, E=12, F=9, G=14, H=5, I=2, J=10, K=3, L=13, M=8

    Solution 2:   A=1, B=3, C=8, D=12, E=5, F=10, G=14, H=4, I=9, J=2, K=6, L=11, M=13
        A=13, B=11, C=6, D=2, E=9, F=4, G=14, H=10, I=5, J=12, K=8, L=3, M=1
        A=3, B=9, C=10, D=8, E=1, F=2, G=14, H=12, I=13, J=6, K=4, L=5, M=11
        A=11, B=5, C=4, D=6, E=13, F=12, G=14, H=2, I=1, J=8, K=10, L=9, M=3
        A=9, B=13, C=2, D=10, E=3, F=6, G=14, H=8, I=11, J=4, K=12, L=1, M=5
        A=5, B=1, C=12, D=4, E=11, F=8, G=14, H=6, I=3, J=10, K=2, L=13, M=9

    Solution 3:    A=1, B=5, C=12, D=8, E=3, F=4, G=14, H=10, I=11, J=6, K=2, L=9, M=13
        A=13, B=9, C=2, D=6, E=11, F=10, G=14, H=4, I=3, J=8, K=12, L=5, M=1
        A=5, B=11, C=4, D=12, E=1, F=6, G=14, H=8, I=13, J=2, K=10, L=3, M=9
        A=9, B=3, C=10, D=2, E=13, F=8, G=14, H=6, I=1, J=12, K=4, L=11, M=5
        A=11, B=13, C=6, D=4, E=5, F=2, G=14, H=12, I=9, J=10, K=8, L=1, M=3
        A=3, B=1, C=8, D=10, E=9, F=12, G=14, H=2, I=5, J=4, K=6, L=13, M=11

    Solution 4:    A=1, B=6, C=11, D=9, E=2, F=4, G=14, H=10, I=12, J=5, K=3, L=8, M=13
        A=13, B=8, C=3, D=5, E=12, F=10, G=14, H=4, I=2, J=9, K=11, L=6, M=1
        A=6, B=12, C=4, D=11, E=1, F=5, G=14, H=9, I=13, J=3, K=10, L=2, M=8
        A=8, B=2, C=10, D=3, E=13, F=9, G=14, H=5, I=1, J=11, K=4, L=12, M=6
        A=12, B=13, C=5, D=4, E=6, F=3, G=14, H=11, I=8, J=10, K=9, L=1, M=2
        A=2, B=1, C=9, D=10, E=8, F=11, G=14, H=3, I=6, J=4, K=5, L=13, M=12
    Solution 5:    A=2, B=4, C=6, D=13, E=5, F=11, G=14, H=3, I=9, J=1, K=8, L=10, M=12
        A=12, B=10, C=8, D=1, E=9, F=3, G=14, H=11, I=5, J=13, K=6, L=4, M=2   
        A=4, B=9, C=11, D=6, E=2, F=1, G=14, H=13, I=12, J=8, K=3, L=5, M=10
        A=10, B=5, C=3, D=8, E=12, F=13, G=14, H=1, I=2, J=6, K=11, L=9, M=4   
        A=9, B=12, C=1, D=11, E=4, F=8, G=14, H=6, I=10, J=3, K=13, L=2, M=5
        A=5, B=2, C=13, D=3, E=10, F=6, G=14, H=8, I=4, J=11, K=1, L=12, M=9

    Solution 6:    A=2, B=5, C=13, D=6, E=4, F=3, G=14, H=11, I=10, J=8, K=1, L=9, M=12
        A=12, B=9, C=1, D=8, E=10, F=11, G=14, H=3, I=4, J=6, K=13, L=5, M=2
        A=5, B=10, C=3, D=13, E=2, F=8, G=14, H=6, I=12, J=1, K=11, L=4, M=9
        A=9, B=4, C=11, D=1, E=12, F=6, G=14, H=8, I=2, J=13, K=3, L=10, M=5
        A=10, B=12, C=8, D=3, E=5, F=1, G=14, H=13, I=9, J=11, K=6, L=2, M=4
        A=4, B=2, C=6, D=11, E=9, F=13, G=14, H=1, I=5, J=3, K=8, L=12, M=10

    Solution 7:    A=3, B=4, C=5, D=13, E=6, F=12, G=14, H=2, I=8, J=1, K=9, L=10, M=11
        A=11, B=10, C=9, D=1, E=8, F=2, G=14, H=12, I=6, J=13, K=5, L=4, M=3
        A=4, B=8, C=12, D=5, E=3, F=1, G=14, H=13, I=11, J=9, K=2, L=6, M=10
        A=10, B=6, C=2, D=9, E=11, F=13, G=14, H=1, I=3, J=5, K=12, L=8, M=4
        A=8, B=11, C=1, D=12, E=4, F=9, G=14, H=5, I=10, J=2, K=13, L=3, M=6
        A=6, B=3, C=13, D=2, E=10, F=5, G=14, H=9, I=4, J=12, K=1, L=11, M=8

    Solution 8:    A=3, B=6, C=13, D=5, E=4, F=2, G=14, H=12, I=10, J=9, K=1, L=8, M=11
        A=11, B=8, C=1, D=9, E=10, F=12, G=14, H=2, I=4, J=5, K=13, L=6, M=3
        A=6, B=10, C=2, D=13, E=3, F=9, G=14, H=5, I=11, J=1, K=12, L=4, M=8
        A=8, B=4, C=12, D=1, E=11, F=5, G=14, H=9, I=3, J=13, K=2, L=10, M=6
        A=10, B=11, C=9, D=2, E=6, F=1, G=14, H=13, I=8, J=12, K=5, L=3, M=4
        A=4, B=3, C=5, D=12, E=8, F=13, G=14, H=1, I=6, J=2, K=9, L=11, M=10


  4. Agree with BMAD


    If 1 = A...that doesn't work, because Question one is not answer B.
    If 1 = B...that doesn't work, because Question one is B...
    If 1 = D, then 2 = B, which means 4 = A. If that is true, then 3 = D and 5 = D...but that can't be true, since question 1's answer is not A. Therefore 1 != D.
    So 1 = C. This means 3 = B.
        If 2 = A...Then 4 = D, but that can't be, since 4 is D.
        If 2 = B...Then 4 = A, but that can't be, since there aren't 3 answers left to be D
        If 2 = C...Then 4 = B, but that can't be true, because there aren't 2 answers left to be D
        So 2 = D, This means 4 = C
             If 5 = D, that doesn't work, because now answer 4 is wrong
             If 5 = A, that doesn't work because 3 = B
             If 5 = C, that doesn't work, because there aren't 3 answers that are B
             So 5 = B
    Final answer: 1=C, 2=D, 3=B, 4=C, 5=B

  5. The attachment you included is broken...so I don't know if my assumption on the description of the problem is correct, but assuming I read it correctly...the answer is: 

    1320 cm3

    V = (3*sqrt(3)/2)a2h

    We know from the description that h (height) = 11cm

    We can use the other clues to determine a (length of a base edge) = sqrt((320/3) * sqrt(3)) / 2

    So simply plugging it in, we get

    V = (3*sqrt(3)/2)(320*sqrt(3)/12)(11)

    V = (2880/24)(11)

    V = 1320cm3

  6. Might not be minimum...

    But you could deliver the message to Mr. Harvey in AT WORST 50 minutes...or 25 calls.

    Start by calling the 25th person on the list....if their name is earlier (alphabetically) than Mr. Harvey, then call the 49th person on the list (24 further)...if if that person is still earlier than Mr. Harvey, call the 72nd person on the list (23 further)...etc...etc...until you get a person that is later (alphabetically) than him. Once you find someone "later", you simply start calling one at a time between the two...

    You could actually then do a divide and conquer approach once you have it narrowed down, which in the long term would make the search faster...but for a SINGLE instance like the OP...to GUARANTEE the message is delivered, it doesn't matter if you do one at a time or divide and conquer, it would still be at worst 25 calls.

  7. Smart-aleck answer:

    I can take any shape/size paper and crumple it into a ball...VOILA! a single sheet of paper "folded" into a sphere!

    But seriously...I think we're starting to get into Map projections here...

    There's probably a "more correct" answer, the but Goode Homolosine projection is pretty darn close...

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