Question

_*_*_= 54
* * *
_*_*_= 120
* * *
_*_*_= 56
= = = 96 180 21
Plz whole solution

Answer 1

The question is shown below:

$\quad$$\begin{array}{ccccccc}\boxed{}&\times &\boxed{}&\times&\boxed{}&=&54\\ \times &&\times &&\times&&\\ \boxed{}&\times &\boxed{}&\times&\boxed{}&=&120\\ \times &&\times &&\times&&\\ \boxed{}&\times &\boxed{}&\times&\boxed{}&=&56\\ =&&=&&=&&\\ 96&&180&&21&&\end{array}$

We have to fill those boxes with digits 1 to 9 without repeating any.

Solution:

$\quad$$\begin{array}{ccccccc}\boxed{6}&\times &\boxed{9}&\times&\boxed{1}&=&54\\ \times &&\times &&\times&&\\ \boxed{8}&\times &\boxed{5}&\times&\boxed{3}&=&120\\ \times &&\times &&\times&&\\ \boxed{2}&\times &\boxed{4}&\times&\boxed{7}&=&56\\ =&&=&&=&&\\ 96&&180&&21&&\end{array}$

Explanation:

• Along the rows:

1. 6 × 9 × 1 = 54
2. 8 × 5 × 3 = 120
3. 2 × 4 × 7 = 56

• Along the columns:

1. 6 × 8 × 2 = 96
2. 9 × 5 × 4 = 180
3. 1 × 3 × 7 = 21

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Answer 2

Given :   The question is shown below:

$\quad\begin{array}{ccccccc}\boxed{}&\times &\boxed{}&\times&\boxed{}&=&54\\ \times &&\times &&\times&&\\ \boxed{}&\times &\boxed{}&\times&\boxed{}&=&120\\ \times &&\times &&\times&&\\ \boxed{}&\times &\boxed{}&\times&\boxed{}&=&56\\ =&&=&&=&&\\ 96&&180&&21&&\end{array}$

To find :  We have to fill those boxes with digits 1 to 9 without repeating any.

Solution:

in addition to swarup solution , i will add how we can reach to solution step by step .

21 & 56 both must have 7 as factor

we have only one 7 from 1 to 9  and no 7 multiplier

Hence 3rd row  - 3 column must be 7

120 * 180 both must have 5 as factor

we have only one 5 from 1 to 9  and no 5 multiplier

hence 2nd row -  2nd column must be  5

after this  21  = 7  *  3 * 1

if we use 1 in 2nd row 3rd column

then 1 * 5 * ? = 120 => ? = 24

hence 2nd row 3rd column  must be 3

& 1st row 3rd column must be  1

so 2nd row 1st column must be 120/(5 * 3)  = 8

if we see 1st row now we left with 2 number to get multiplication 54

54 = 1 * 54 , 2 * 27 , 3 * 18   ( not Possible)

hence we left with 6 * 9  only

if we use 1st row 1st column as 9 then  96/(9 * 8) is not integer

Hence 1st row 1st column must be 6  & 1st row 2nd column must be 9

now we get  96/(6 * 8) = 2

& 180 /(9 * 5)  = 4

& get the below solution

$\quad\begin{array}{ccccccc}\boxed{6}&\times &\boxed{9}&\times&\boxed{1}&=&54\\ \times &&\times &&\times&&\\ \boxed{8}&\times &\boxed{5}&\times&\boxed{3}&=&120\\ \times &&\times &&\times&&\\ \boxed{2}&\times &\boxed{4}&\times&\boxed{7}&=&56\\ =&&=&&=&&\\ 96&&180&&21&&\end{array}$

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