Math

QuestionComplete the unmagic square with different sums for rows, columns, and diagonals using digits 1-9:
8 & & 9 & 7 & 1 & & 6
Choose from options A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. The unmagic square is a3x3 square. . Each of the digits1 through9 must be used once and only once.
3. The sums of the rows, columns, and diagonals must all be different.

STEP 2

We need to calculate the sums of the rows, columns, and diagonals for each option and check if they are all different.

STEP 3

Start with option A. Calculate the sums of the rows, columns, and diagonals.
For the rowsRow1=8++9=21Row1 =8 + +9 =21Row2=3+7+2=12Row2 =3 +7 +2 =12Row3=1+5+6=12Row3 =1 +5 +6 =12For the columnsColumn1=8+3+1=12Column1 =8 +3 +1 =12Column2=+7+5=16Column2 = +7 +5 =16Column3=9+2+6=17Column3 =9 +2 +6 =17For the diagonalsDiagonal1=8+7+6=21Diagonal1 =8 +7 +6 =21Diagonal2=9+7+1=17Diagonal2 =9 +7 +1 =17

STEP 4

Check if all the sums calculated in3 are different.We can see that the sums of Row1 and Diagonal1 are the same (21), and the sums of Row2, Row3, and Column1 are the same (12). So, option A does not satisfy the conditions of an unmagic square.

STEP 5

Repeat3 and4 for option B.
For the rowsRow1=8+5+9=22Row1 =8 +5 +9 =22Row2=2+7+4=13Row2 =2 +7 +4 =13Row3=1+3+=10Row3 =1 +3 + =10For the columnsColumn1=8+2+1=11Column1 =8 +2 +1 =11Column2=5+7+3=15Column2 =5 +7 +3 =15Column3=9+4+=19Column3 =9 +4 + =19For the diagonalsDiagonal1=8+7+=21Diagonal1 =8 +7 + =21Diagonal2=9+7+1=17Diagonal2 =9 +7 +1 =17

STEP 6

Check if all the sums calculated in5 are different.We can see that all the sums are different. So, option B satisfies the conditions of an unmagic square.

STEP 7

Since we have found an option that satisfies the conditions, we do not need to check the remaining options.The solution is option B. \begin{tabular}{|l|l|l|} \hline &5 &9 \\ \hline2 &7 &4 \\ \hline1 &3 &6 \\ \hline\end{tabular}

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