Write the numbers from 1 to 7 in the circles without repeating the sum of the numbers in a line should be12 .
Answers
Given : 1,2,3,4,5,6 and 7 numbers & circles
To find : Put the numbers so that the each straight line of the three numbers add up to the three numbers
Solution:
Let say A , B , C , D , E , F & G are 7 numbers from 1 to 7
& D is in center
A & G , B & F , C & E are opposite
A + D + G = B + D + F = C + D + E
=> A + G = B + F = C + E
Adding all numbers
A + B + C + D + E + F + G + 2D
( A + B + C + D + E + F + G = 28 ( 1 to 7 sum)
= 28 + 2D
28 + 2D is Divisible by 3 as sum of 3 Equal sums
Hence
D = 1 , 4 , 7
Case 1
D = 1
28 + 2D = 30 Sum of Each = 10 , D = 1
=> A + G = B + F = C + E = 9
only possible solution
2 + 7 = 3 + 6 = 4 + 5
Case 2
D = 4
28 + 2D = 36 Sum of Each = 12 , D = 4
=> A + G = B + F = C + E = 98
only possible solution
21+ 7 = 2 + 6 = 3 + 5
Case 3
D = 7
28 + 2D = 42 Sum of Each = 14 , D = 7
=> A + G = B + F = C + E = 97
only possible solution
1 + 6 = 2 + 5 = 3 + 4
Hence 3 possible Solutions with center numbers 1 , 4 , 7