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Posts posted by jasen

  1. At a class, the students are going to choose a leader.
    The class has 3 groups of students.
    Each group contains 4 students.
    so total students are 12.
    After discussion, they determine this rule :

    each students have to vote 1 from each group.
    so each students have to vote for 3 persons.
    example: if the groups are [a,b,c,d] [e,f,g,h] [i,j,k,l]
    each student have to choose 1 from [a,b,c,d], 1 from [e,f,g,h], and 1 from [i,j,k,l]

    If someone break the rule, his votes is disqualified.

    (To simplify the problem, lets write just initials of the students,
    since there is no 2 students has same initials)

    here are the votes

     1. [c,d,f]     2. [a,g,c]     3. [d,h,l]    4. [b,e,d]     
     5. [f,j,g]     6. [g,j,i]     7. [j,i,a]    8. [j,a,f]
     9. [b,h,k]     10.[l,c,d]     11.[a,h,l]    12.[g,e,b]

    there is 1 vote is disqualified.

    The Questions :

    • Determine each group members
    • Determine which vote is disqualified.
  2. A Traveler is going to a town, but he must pass a strange village,
    From the village there are 3 streets, only 1 street leads him to the town,
    He doesn't know which street he must choose,
    The villagers are giving the streets name with numbers written in local symbols,
    The traveler can not read the symbols.

    He asked 11 villagers, and he received 11 different answers

    1st villager : "Take the street with a cube number."
    2nd villager : "Take the street with lowest number."
    3rd villager : "Take the street with middle number."
    4th villager : "Take the street with higest number."
    5th villager : "If you divide the right street number (RSN) with 8, the remaining is 7."
    6th villager : "If you divide RSN with 24, the remaining is 15."
    7th villager : "If you divide RSN with 12, the remaining is 3."
    8th villager : "If you divide RSN with 4, the remaining is 3."
    9th villager : "If you divide RSN with 6, the remaining is 3."
    10th villager : "If you divide RSN with 5, the remaining is 2."
    11th villager : "If you divide RSN with 7, the remaining is 6."

    After finding so varying answer, he decided to ask the chief of the village,

    The chief than giving him this right information :

    "we are numbering streets with numbers between 10 to 50,
     The left street has lowest number,
     The right street has higest number,
     The front street has bigger number than left street,
     3 villagers give you useless answers,
     4 villagers give you right answers,
     and 4 villagers give you wrong answers"

    What are the street numbers ? Which street he must choose ?

    Note :

    Useless answer means if you know the numbers, the answer is right to all numbers, so it is useless.
    Wrong answer means the answer is leading you to 1 wrong street or 2 wrong streets,
    right answer means the answer is leading you only 1 street, and it is the right street.

  3. To avoid the customers' disappointement, the bartender comes up with a solution.
    He gives each man a glass of cocktail, and explains :

    If each letter represents a digit, we can write it like this :

    1 pepsi + 1 cocacola = 1 cocktail  -> 1 *  40497 + 26212681 = 26253178
    2 pepsi + 1 cocacola = 1 cocktail  ->  2 * 27264 + 58535813 = 58590341
    3 pepsi + 1 cocacola = 1 cocktail  -> 3 * 20239 + 54515481 = 54576198
    4 pepsi + 1 cocacola = 1 cocktail  -> 4 * 18153 + 64606420 = 64679032
    5 pepsi + 1 cocacola = 1 cocktail  -> 5 * 12149 + 73707350 = 73768095

  4. Thanks Plasmid for your attempt to test this conjecture effectively to 1 trillion.

    There is a way to check whether a number is pentagonal, square or triangle, by find out the n-th of the number.

    n-th Pentagon x = (1+sqrt(1+24* x)) / 6,  (if n is integer so the number is pentagonal)
    n-th Square x = sqrt x,                            (if n is integer so the number is square number)
    n-th Triangle x = (sqrt(8*x + 1)-1)/2,         (if n is integer so the number is triangle)

  5. There was 25 kids in a class, every kids had some best friends.
    To simplify the problem, Let's call each kids with their initial name.
    here is a list of kids best friends.

    a : [l,h]
    b : [k,m,i]
    c : [f,l,n,j]
    d : [g,m,o]
    e : [h,n]
    f : [c,m,q]
    g : [d,n,r,p]
    h : [a,k,q,s,o,e]
    i : [b,l,r,t]
    j : [c,m,s]
    k : [u,r,h,b]
    l : [u,w,s,i,c,a]
    m : [f,b,d,j,t,x,p,v]
    n : [y,w,q,g,c,e]
    o : [x,r,h,d]
    p : [w,m,g]
    q : [x,n,h,f]
    r : [u,k,g,i,o,y]
    s : [v,l,h,j]
    t : [w,m,i]
    u : [l,r]
    v : [k,m,s]
    w : [p,l,n,t]
    x : [q,m,o]
    y : [r,n]

    One day all kids was outside the class room except "a".
    then his teacher asked "a" to call one of his best friend to enter the room, "a" called "l". 
    then the teacher asked "l" to call one of his best friend outside to enter the room, and so on.
    after all the call chain, there was no more kids outside, and "s" was the last kids called.

    determine the call chain !

  6. 5 man enter a bar.
    1st man order 1 Pepsi + 1 Coca cola 
    2nd man order 2 Pepsi + 1 Coca cola 
    3rd man order 3 Pepsi + 1 Coca cola 
    4th man order 4 Pepsi + 1 Coca cola 
    5th man order 5 Pepsi + 1 Coca cola 
    But they ask the bartender to give them same amount of drinks.

    as a logician and mathematician the bartender comes with a solution,
    he gives each man a glass of cocktail, and they all happy.

    Explain why the bartender gives each man a glass of cocktail ?

  7. 21 hours ago, Pickett said:
      Reveal hidden contents

    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:

    ------ cut  ----


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

    Reflection works vertically

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