Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Math Question?

In order to win the grand prize, paul has to crack this secret code. clues:

a. the third is greater than the second digit

b. the difference between the third and fourth digits is 3

c. when the sum of all numbers is divided by 5, it has a remainder of 3

d. when the sum of all the numbers is divided by 6, it has a remainder of 3​

2 Answers

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  • Alan
    Lv 7
    1 month ago
    Favorite Answer

    1st , you need to clarify if 

    the difference between the 3 and 4th digits is 3 

    implies whether you mean 

    3rd -4th  = 3 

    or 

    4th - 3rd = 3 

    if you don't care , then 

    so the five digit number 

    77856  

    works

    the sum = 33

    33/6 has remainder 3

    33/5 has remainder 3

    8> 7

    8-5 = 3

    5-8 = -3 

    I first checked for 4 digit number and 

    it seems impossible. 

    so if it's a 4 digit number 

    then  abcd 

    c> b 

    c-d =  3 

    (a+b+c+d)/5  has remainder 3 

    (a+b +c +d)/6 has remainder 3 

    since a, b, c, and d are all less than 9 

    there sum is  36 or less   

    so 1st sum say one of the following is true 

    (a+ b+ c+  d) = 8,13,18,23, 33 

    2nd sum says 

    (a+b+c +d ) = 9,15, 21,27, 33

    What the common value , it is 33 

    so you know (a+b+c+d) =33   

    so if 3 of digits were so possible digits include

    Not caring about order yet,  

    9,9,9,6

     9,9,8,7 (but no two digits are 3 apart) 

    9,8,8,8  (but no two digits are 3 apart) 

    9,7,9,8  (but no two digist are 3 apart) 

    so 9,9,9,6 are a good combination

    but no combination of these numbers  can meet the other criteria  

    so it must a 5 digits number  

    a+b+c+ d+ (d-3) = 33 

    or a+ b+ c+d +(d+3) = 33 

    a+b +c +2d  = 36 

    a+ b+ c + 2d =30 if d = 4, 

    then a+ b+ c =  28 (impossible ) or a+ b+ c =  22   

    then all other digits must be at least 7 and so   

    could find one worked 

    but then a saw one the worked if  d = 5  

    77856

    the sum = 33 

    33/6  has remainder 3 

    33/5  has remainder 3 

    8> 7 

    8-5 = 3 

    5-8 = -3 

  • 1 month ago

    c > b

    c - d = 3

    (a + b + c + d )/5 = x + 3

    (a + b + c + d)/6 = y + 3

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