put the numbers 1234567 in the circle so that each straight line of three numbers add up to the same total
Answers
Answer:
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Given: 1,2,3,4,5,6 and 7 numbers & circles
To find: Put the numbers so that 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 the sum of 3 Equal sums
Hence
D = 1 , 4 , 7
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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
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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
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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
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Hence 3 possible Solutions with center numbers 1, 4, 7.
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