Question

Put first seven multiples of 2 (2, 4, 6, 8,10, 12, 14) in the circles such that eachstraight line of three circles adds upto the same number.​

Answer 1

Given : seven multiples of 2 (2, 4, 6, 8,10, 12, 14)  & 7 Circle

To find :  Put numbers such that each straight line of three circles adds up to the same number.​

Step-by-step explanation:

Assuming Circle Configuration As below

Let say numbers are  A , B , C  ,  D , E  ,  F , G

                       A⊕

       B⊕         C⊕          ⊕D

E⊕                 F⊕                 ⊕G

A + B + E = A + D+ G =  B + C + D  = A + C + F  = E + F + G

Adding all

= A +  2 (A + B + C + D + E + F + G)

= A + 2(56)

=A + 112

Sum of Each line is Equal Hence  A + 112 should be divisible by 5

=> A =  8  

Sum = 8 + 112 = 120

Sum of Each = 120/5  = 24

There can be Many possible Solutions  :

Here is one of them

                      ⊕8

       2⊕        ⊕12          ⊕10

14⊕               ⊕4                 ⊕6

Another possibility

           A⊕                         B⊕        

C⊕                    ⊕D                       E⊕                

       

         F⊕                          ⊕G

A + D + G = C + D + E = B + D + F

Adding all = (A + B + C + D + E + F + G ) + 2D

= 56 + 2D

D = 2   or    8    or  14  

sum of each row = 20 , 24 , 28

           14⊕                         B8        

6⊕                    ⊕2                       E12                

       

         10⊕                          ⊕4

           14⊕                         B6        

4⊕                    ⊕8                       E12                

       

         10⊕                          ⊕2

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