🧠Sunday Brain Teasers !! - āˇƒāˇ”āļ¸āˇāļąāˇāļœāˇš āļšāˇāļ§āˇš āļœāˇāļą āˇ„āˇœāļēāļąāˇŠāļą āˇ€āļģ⎙āļąāˇŠ gembo! ... (IQ)

āļąāˇ‘ āļŠāļ§ āˇ€āļŠāˇ āļœāˇœāļŠāļšāˇŠ āļŊ⎜āļšāˇ”āļē⎒ . Hint āļ‘āļšāļšāˇŠ āļ¯āˇ™āļąāˇŠāļąāļ¸āˇŠ āļ´āˇ”āļŊ⎔⎀āļąāˇŠ āļąāļ¸āˇŠ ⎄⎒āļ­āļ´āļąāˇŠ .
4 x 4 āļ‘āļšāˇŠāļšāļšāˇŠ āļ¯āˇ™āļąāˇŠāļąāļ¸āˇŠ . āļ‘āļšāˇš āļ•āļąāˇ‘āļ¸ 2x 2 āļšāˇœāļ§āˇƒāļš B āļ”āļ­āˇŠāļ­āˇš ⎀⎙āļą āˇ€āˇ’āļ¯āˇ’āļēāļšāļ§ āļ´āˇ”āļģ⎀āļŊ āļ¯āˇ“āļ´āļ‚ āļļāļŊāļąāˇŠāļą .

B R B B
R X X X
R X X X
B X X X

āļ¸āˇšāļšāˇš x ⎀⎙āļąāˇ”⎀āļ§ B , R āļ¯āˇāļ´āļ‚ āļļāļŊāļąāˇŠāļą āˇ„āļģ⎒ ⎀⎒āļ¯āˇ’āļēāļšāļ§ . ..
648 ?
 

dilann

Well-known member
  • āļēāļšāˇ āļ”āļē āļ¸āļ¸ āļ¯āˇ”āļąāˇŠāļą 4x4 āļ‘āļšāˇš , ⎄⎐āļ¸ 2x2 āļšāˇœāļ§āˇ”⎀āļšāˇŠ āļ‡āļ­āˇ”āļŊ⎙āļ¸ B āļ’āˇ€āˇ āļ”āļ­āˇŠāļ­āˇš ⎀⎙āļą āˇ€āˇ’āļ¯āˇ’āļēāļšāļ§ B , R ⎀āļŊ⎒āļąāˇŠ āļ´āˇ”āļģ⎀āļąāˇŠāļą āļšāˇ’āļēāļŊāˇ āļšāˇ’āˇ€āˇŠāˇ€āˇš .
     
    āļēāļšāˇ āļ”āļē āļ¸āļ¸ āļ¯āˇ”āļąāˇŠāļą 4x4 āļ‘āļšāˇš , ⎄⎐āļ¸ 2x2 āļšāˇœāļ§āˇ”⎀āļšāˇŠ āļ‡āļ­āˇ”āļŊ⎙āļ¸ B āļ’āˇ€āˇ āļ”āļ­āˇŠāļ­āˇš ⎀⎙āļą āˇ€āˇ’āļ¯āˇ’āļēāļšāļ§ B , R ⎀āļŊ⎒āļąāˇŠ āļ´āˇ”āļģ⎀āļąāˇŠāļą āļšāˇ’āļēāļŊāˇ āļšāˇ’āˇ€āˇŠāˇ€āˇš .
    B R B B
    R R R B
    R B R R
    B B B R
     
    ⎄āļģ⎒ . . āļ­āˇ€ ⎀⎒āļ¯āˇ’āļēāļšāļ§ āļ’ X āļ´āˇ”āļģ⎀āļ´āļąāˇŠ
    āļ…āļŠāˇš āļ¸āļ§ āˇ„āļ¯āˇāļœāļąāˇŠāļą āļļ⎑ āļļāļ‚
    āļšāˇ’āļēāļŊ āļ¯āˇ’āļēāļąāˇŠāļšāˇœ āļ‹āļ­āˇŠāļ­āļģ⎚ āļœāļ­āˇŠāļ­ āˇ€āˇ’āļ¯āˇ’āļē
     

    dilann

    Well-known member
  • āļ…āļŠāˇš āļ¸āļ§ āˇ„āļ¯āˇāļœāļąāˇŠāļą āļļ⎑ āļļāļ‚
    āļšāˇ’āļēāļŊ āļ¯āˇ’āļēāļąāˇŠāļšāˇœ āļ‹āļ­āˇŠāļ­āļģ⎚ āļœāļ­āˇŠāļ­ āˇ€āˇ’āļ¯āˇ’āļē
    āļ­āˇ€ ⎀⎒āļ¯āˇ’ āļąāˇ‘ āļ‰āļ­āˇ’āļąāˇŠ X āļ´āˇ”āļģ⎀āļąāˇŠāļą āļ”āļē āļ¯āˇ“āļŊ āļ­āˇ’āļēāļą āļ‘āļšāˇš . đŸĨą

    B R B B
    R
    R R B
    R B R R
    B B B R

    āļąāˇ’āļšāļąāˇŠ ⎄⎒āļ­āļ´āļąāˇŠ . āļ”āļē āˇƒāˇ”āļ¯āˇ” āļ´āˇšāļŊ⎒ āļ¯āˇ™āļšāļ§ āļ…āļ´āˇ’āļ§ āļšāˇāļ¸āļ­āˇ’ ⎀⎒āļ¯āˇ’āļēāļ§ āļŊ⎒āļēāļąāˇŠāļą āļ´āˇ”āļŊ⎔⎀āļąāˇŠ . ⎄⎐āļļ⎐āļē⎒ āļ¸āˇāļ¯ āļ§āˇ’āļš fixed āļ’ āļ‘āļš āļ‘āļš āˇ€āˇ’āļ¯āˇ’āļēāļ§ .
    āļ’ āˇ€āˇ’āļ¯āˇ’āļēāļ§ āˇ„āˇ’āļ­āļ´āļąāˇŠ
     
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    āļ­āˇ€ ⎀⎒āļ¯āˇ’ āļąāˇ‘ āļ‰āļ­āˇ’āļąāˇŠ X āļ´āˇ”āļģ⎀āļąāˇŠāļą āļ”āļē āļ¯āˇ“āļŊ āļ­āˇ’āļēāļą āļ‘āļšāˇš . đŸĨą

    B R B B
    R
    R R B
    R B R R
    B B B R

    āļąāˇ’āļšāļąāˇŠ ⎄⎒āļ­āļ´āļąāˇŠ . āļ”āļē āˇƒāˇ”āļ¯āˇ” āļ´āˇšāļŊ⎒ āļ¯āˇ™āļšāļ§ āļ…āļ´āˇ’āļ§ āļšāˇāļ¸āļ­āˇ’ ⎀⎒āļ¯āˇ’āļēāļ§ āļŊ⎒āļēāļąāˇŠāļą āļ´āˇ”āļŊ⎔⎀āļąāˇŠ . ⎄⎐āļļ⎐āļē⎒ āļ¸āˇāļ¯ āļ§āˇ’āļš fixed āļ’ āļ‘āļš āļ‘āļš āˇ€āˇ’āļ¯āˇ’āļēāļ§ .
    āļ’ āˇ€āˇ’āļ¯āˇ’āļēāļ§ āˇ„āˇ’āļ­āļ´āļąāˇŠ
    1024 x 512 āļ¯ āļ‹āļ­āˇŠāļ­āļģ⎚?
     
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    kohomda gaththe ?

    āļ”āļēāˇ āļšāˇ’āļēāļ´āˇ” ⎀⎒āļ¯āˇ’āļēāļ§ āˇ„āˇāļ¯āˇ”⎀⎙
    āļ‹āļŠāļ¸ āļ´āˇšāļŊ⎒āļēāļ§ permutation āļ¯āˇāļ¸āˇŠāļ¸
    2^10
    āļ‹āļŠ āļ´āˇšāļŊ⎒āļē āļ…āļē⎒āļąāˇŠ āļšāˇ…āˇāļ¸, āļ­āˇ“āļģ⎔⎀āļšāļ§ āļ‘āļąāˇŠāļąāˇ™ āļ‘āļ­āļšāˇœāļ§ 9 āļē⎒ āļąāˇ™
    2^9 āļ¯āˇāļ¸āˇŠāļ¸

    Permutations with Repetition​


    āļ…āļģ āļœāˇāļĢāļ­āˇŠ ⎄⎐āļ¯āˇ”⎀. āļŠāļē⎙ āˇ„āˇœāļģ āļ´āˇāļģ⎙āļąāˇŠ āļąāˇ™ ⎄⎐āļ¯āˇ”⎀⎙
    y = āļ´āˇœāļšāˇ”āļĢ⎙ ⎄⎒āļ§āļ´āˇ” āļœāˇ™āļ¸āˇŠāļļ⎜ āļ§āˇ’āļš
    x = ⎀āļģāļšāļ§ āļœāˇ’āļŊāļ´āˇ” āļœāˇ™āļ¸āˇŠāļļ⎜ āļœāļĢāļą
    3(3(3(y-x) - x)-x) = x
    27y = 40x


    @dilann
     
    Last edited:
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    dilann

    Well-known member
  • āļ”āļēāˇ āļšāˇ’āļēāļ´āˇ” ⎀⎒āļ¯āˇ’āļēāļ§ āˇ„āˇāļ¯āˇ”⎀⎙
    āļ‹āļŠāļ¸ āļ´āˇšāļŊ⎒āļēāļ§ permutation āļ¯āˇāļ¸āˇŠāļ¸
    2^10
    āļ‹āļŠ āļ´āˇšāļŊ⎒āļē āļ…āļē⎒āļąāˇŠ āļšāˇ…āˇāļ¸, āļ­āˇ“āļģ⎔⎀āļšāļ§ āļ‘āļąāˇŠāļąāˇ™ āļ‘āļ­āļšāˇœāļ§ 9 āļē⎒ āļąāˇ™
    2^9 āļ¯āˇāļ¸āˇŠāļ¸

    Permutations with Repetition​


    āļ…āļģ āļœāˇāļĢāļ­āˇŠ ⎄⎐āļ¯āˇ”⎀. āļŠāļē⎙ āˇ„āˇœāļģ āļ´āˇāļģ⎙āļąāˇŠ āļąāˇ™ ⎄⎐āļ¯āˇ”⎀⎙
    3(3(3(x-y) - x)-x) = x
    27y = 40x
    ⎄āļģ⎒ .. āļ”āļē āļ‰āļ­āˇ’āļąāˇŠ āļ‹āļļ ⎄āļ¯āļąāˇŠāļąāˇš :rofl:
     
    ⎄āļģ⎒ .. āļ”āļē āļ‰āļ­āˇ’āļąāˇŠ āļ‹āļļ ⎄āļ¯āļąāˇŠāļąāˇš :rofl:
    āļ…āļ¸āˇāļģ⎔⎀⎙āļąāˇŠ āļļāļŠ āļœāˇāļŊ ⎄⎐āļ¯āˇ”⎀⎙
    āļœāˇāļĢāļšāˇŠ ⎄āļ¯āˇāļœāļąāˇŠāļą āļļ⎐āļģ⎔⎀ āļœāˇ’āļēāˇāļ¸ āˇ„āļģ⎒āļēāļ§ āļ…āļ´āˇŠāˇƒāļ§āˇŠ āļēāļąāˇ€
    ⎄āļ­āļģ⎀⎙āļąāˇ’ āļœāˇāļĢ āļąāļ¸āˇŠ āļ”āļēāˇ āļšāˇ’āļēāļ´āˇ” āļ…āļē⎒āļŠāˇ’āļēāˇ āļ‘āļš āļąāˇ’āˇƒāļē⎒ ⎄⎐āļ¯āˇ”⎀⎙
    āļąāˇāļ­āˇŠāļ­āļ‚ āˇ„āˇ’āļ­āˇ āļœāļąāˇŠāļąāļ¸ āļļ⎑ āļ¸āļ§
     

    imhotep

    Well-known member
  • Mar 29, 2017
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    Noted this during the weekend but was busy away from home and also people should think and reply.

    Not difficult if you think. eg the frog problem.

    Lets say we had F frogs in the pond. The crane visits every Sunday and ate a fixed number of frogs, say x.

    The natural growth is a factor of 3.... and we assume that there are no natural deaths.
    Given constraint 100 ≤ x ≤ 150

    First week - Start F frogs, Crane eats x, remainder F-x
    Second week - Frogs multiply by a factor of 3, so Start count is 3(F-x). remainder 3(F-x) - x
    Third week Start count is 3 (3(F-x) -x) with a remainder 3 (3(F-x) -x) - x
    Fourth week Start count is 3 (3 (3(F-x) -x) - x) with a remainder of 3 (3 (3(F-x) -x) - x) - x

    Since there's none left 3 (3 (3(F-x) -x) - x) - x = 0
    which simplifies to F = 40 x / 27
    with the constraint the ossible answer is F = 120 with x = 81.
     
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