Now fill in the given magic square with numbers 11 to 19 so that sum of numbers each row and column is 45
Answers
Step-by-step explanation:
18. 11. 16.
13. 15. 17.
14. 19. 12.
Answer:
The required magic square is
12 17 16
19 15 11
14 13 18
Step-by-step explanation:
The numbers with which we have to form the magic square are numbers between 11 and 19.
So the numbers we have to use are 11, 12 , 13 , 14, 15, 16 , 17, 18 and 19.
The sum of numbers of each row and each column is 45.
So by trail and inspection we can see that the combinations of three of the above numbers which when added give a sum of 45 are
i) 11 + 15 + 19 = 45
ii) 11 + 16 + 18 = 45
iii) 12 + 19 + 14 = 45
iv) 12 + 15 + 18 = 45
v) 12 + 17 + 16 = 45
vi) 13 + 14 + 18 = 45
vii) 13 + 15 + 17 = 45
viii) 14 + 15 + 16 = 45
The most common number in all the combinations is 15 which is in 4 of the combinations
Therefore we can keep 15 in middle.
The next most common number which is also the least is 12.
So we start of with 12 in the first position. So we can use for the first row 12, 14, 19 or 12, 14, 19 and we can use either for the first column.
We take 12, 17, 16 as the first row and 12, 19, 14 as the first column
As 15 has been taken as the middle number therefore the first diagonal from left to right will be filled as 12, 15, 18.
We can fill up the rest of the remaining two spaces in third column and the third row with 11 and 13 respectively.
12 17 16
19 15 11
14 13 18