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jasen

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Posts posted by jasen

  1. @DejMar 

    1st question
    1 5 6 3 2 7 = 1 6 5 2 3 6 = 5 1 6 7 2 3 = 5 6 1 2 7 3 = 6 1 5 7 3 2 = 6 5 1 3 7 2   1st solution
    2 3 7 5 1 6 = 2 7 3 1 5 6 = 3 2 7 6 1 5 = 3 7 2 1 6 5 = 7 2 3 6 5 1 = 7 3 2 5 6 1  2nd solution

    2nd question
    2  9 12  4  3 18 = 2 12  9  3  4 18 = 9  2 12 18  3  4 = 9 12  2  3 18  4 = 12  2  9 18  4  3 = 12  9  2  4 18  3 = 1st solution
    3  4 18  9  2 12 = 3 18  4  2  9 12 = 4  3 18 12  2  9 = 4 18  3  2 12  9 = 18  3  4 12  9  2 = 18  4  3  9 12  2 = 2nd solution

    Just Rotation and reflection of the circle.


     

     

  2. 1. Easy Puzzle

    Put numbers 1,2,3,5,6,7 to each point, so :

    I.  The sum of points in every circle  are equal,  (A+E+F+C = B+E+D+C = A+D+F+B)

    II.  A+B+C = D+E+F

    There are 2 solutions.

     

    2 .Harder Puzzle

    Find the value of x, then put number 2,3,4,9,12,x to each point, so :

    I.  The product of points in every circle  are equal,  (A*E*F*C = B*E*D*C = A*D*F*B)

    II.  A*B*C = D*E*F

    There are 2 solutions.

    3 circles.jpg

  3. Spoiler


    Possibilities

    1  L:Natalia  R:Empty  = true stat : 1,3 
    2  L:Lion     R:Empty  = True Stat : 2
    3  L:Empty    R:Natalia = True Stat : 3
    4  L:Empty    R:Lion   = True Stat : 2,4
    5  L:Natalia  R:Lion   = True stat : 1,2,3,4
    6  L:Lion     R:Natalia = true stat : 3,4
    7  L:Lion     R:Lion   = true stat : 2,4
    8  L:Empty    R:Empty  = True stat : none

    Possibility number 2 and 3 are quailified
    So choose right door, since you may find Natalia or empty room, at least you will not eaten by lion.
     

     

  4. Similar, but a bit harder puzzle :

    A father left 102 goats to his three sons. He promised 1/2 of the goats to the oldest son, 1/5 to the middle son, and 1/13 to the youngest son (maybe step son, just get a bit heritage :) ). But the sons could not divide 102 evenly. Then they call their uncle, after thinking a while the uncle come with a solution, and as thanks they give the uncle 1 goat, what is the uncle solution ?

  5. A father left 45 goats to his three sons. He promised 1/2 of the goats to the oldest son, 1/4 to the middle son, and 1/6 to the youngest son. But the sons could not divide 45 evenly. Then they call their uncle, after thinking a while the uncle come with a solution, and as thanks they give the uncle 1 goat, what is the uncle solution ?

  6. 16,363636 minutes

    Spoiler

     

    The hour and minute hands are superimposed only when their angle is the same.
    in 12 hour, hour and minute hands superimposed 11 times.

    so time between 2 superimposed is 12/11 hour = 65.454545... minutes

    greatest negative (receding) speed when minute and hour hand form  -90 deg.
    greatest positive (approaching) speed  when minute and hour hand form 0 deg.

    because 1 circle is 360 deg, so :
    time from negative to positive speed speed is

    (12/11)/4 hour = 16,363636 minutes

     

     

  7. If we make sequences of the numbers, we  get this pattern :

    Month

    0

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    sequence

    1

    1

    3

    5

    11

    21

    43

    85

    171

    341

    683

    1365

    2731

    This pattern is called Jacobsthal numbers, Like Fibonacci numbers,  sequence follow the rule :

    The first two numbers in the  sequence are  0 and 1, then each following number is found by adding the number before it to twice the number before that.

    In math expression : Jn =  2*J(n-2) +  J(n-1)

    The formula to find the x-th number  is  Jn = ((2n)-(-1)n) / 3

    So after 1 year there are J13 = (213 + 1) / 3 = 2731 pairs of rabbits

  8. A man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets two new pair which from the second month on becomes productive?

    This problem states several important factors:

    •     Rabbits take one month to grow up
    •     After they have matured (for one month) it takes a pair of rabbits one more month to produce their first 2 pairs of newly born rabbits.
    •     We assume that rabbits never die
    •     We assume that whenever a new pair of rabbits is produced, it is always a male and a female
    •     We assume that these rabbits live in ideal conditions
    •     The problem begins with just one pair of newly born rabbits (a male and a female). Given all

    this information, how many pairs of rabbits will there be in one year (12 months)?

  9. 16 hours ago, DejMar said:
      Reveal hidden contents

    Given that the first mathematician was unable to know the ages of the four children, the sum of the ages occurs multiple times for different sets of integer ages where the sum of the reciprocals equals the multiplicative identity. This only occurs where the sum is 22 (which must be the age of the first mathematician's sister). These values are: (8,8,4,2), (6,6,6,2), (12,4,3,3).
    Given the oldest two are twins reduces this to two possibilities:  (8,8,4,2) and (6,6,6,2). The first set is likely the intended answer, though the second can not be dismissed without consideration. (It is a fact that a child can be born less than a year after an older sibling, thus for a short period they can have the same age). Still, considering that a single solution is sought, the ages themselves are to be considered the compose the twins (as opposed to the children), and thus (8,8,4,2) would be the answer.


     

    Right Answer, but you make a bit miscalculation. sum of 6,6,6,2 is 20, not 22.

    Spoiler

    1st Clue  : Sum of their multiplicative inverse is 1

    All age possibility are

    4th child

    3rd child

    2nd child

    1st child

    sum ages

    2

    3

    7

    42

    54

    2

    3

    8

    24

    37

    2

    3

    9

    18

    32

    2

    3

    10

    15

    30

    2

    3

    12

    12

    29

    2

    4

    5

    20

    31

    2

    4

    6

    12

    24

    2

    4

    8

    8

    22

    2

    5

    5

    10

    22

    2

    6

    6

    6

    20

    3

    3

    4

    12

    22

    3

    3

    6

    6

    18

    3

    4

    4

    6

    17

    4

    4

    4

    4

    16

    2nd Clue  : Sum of their age is your sister age

    Because “mat 1” said that knowing the total (from the age of her sister) did not help, we know that knowing the sum of the ages does not give a definitive answer; thus, there must be more than one solution with the same total.

    Only three sets of possible ages add up to the same totals:

    2

    4

    8

    8

    22

    2

    5

    5

    10

    22

    3

    3

    4

    12

    22

    3rd clue : 2 oldest are twin

    “mat 2” concludes that the correct solution is 8,8,4,2.

     

     

     

  10. 2 mathematicians meet at their school reunion.
    mat 1 : Hey old friend, I heard you have 4 child, How old are they?
    mat 2 : Sum of their multiplicative inverse is 1, and sum of their age is your sister age.
    mat 1 : But, I still don't know their ages.
    mat 2 : 2 oldest are twin.
    mat 1 : ok, I know know.

  11. statistically it is uniform. 

    1000 places of Pi

    3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

    1=116, 2=103, 3=103, 4=93, 5=97, 6=94,7=95, 8=101, 9=106, 0=93  total digits 1001

    Also for base2, 100008 first digits, have 50052 1

  12. I think bubbled is right, 
    "Sorting like" strategy, without "real sorting"  will not work.

    I have proposed this "Sorting like" strategy, exactly like plasmid.

    How about this :

    Hidden Content

    but then I realize it was not working. I've tested it using dev-C++.
    the chance to find your name is only 50%, the same chance with random way opening boxes.

    in my program : box numbered from 0 to 9, and your number is random from 0 to 9. You can only open 5 boxes to find your name.

     

    findNamesInBoxes.gif

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