Put all following numbers into box so as no number should be left and no one should be repeated 1, 2,3,4,5,6,7,8,9.
Answers
Step-by-step explanation:
total way to put
9!= 9×8×7×6×5×4×3×2= 362880
Given : _ _x_=_ _+_ _=_ _ ( 9 blanks paces )
To find : Blank spaces to be filled with 1 to 9 Digits
Solution:
Complete Question
AB
* C
____
DE
+ FG
______
HI
Here AB * C = DE ( is one operation)
DE + FG = HI ( another operation)
there is no linkage directly between AB & HI
A to I digit 1 to 9
17 x 4 = 68 + 25 = 93
17 * 4 = 68
68 + 25 = 93
17
* 4
____
68
+ 25
______
93
Here is how we reached to solution
All digits used from 1 to 9
ab* c = de
de + fg = hi
1 to 9 digit
hi two digit
b , c can not be 1 or 5
as ab * 1 = ab => ab = de ( with same digits)
a1 * c will end with c a5 * c will end with 5 or 0
ab * 5 will end with 0 or 5 ( 0 not available , 5 will be repeated digit in c & i)
Let s check all possible
11 , 12 * 1 , 12 * 2 , 12 * 3 = 36 , 12 * 4 = 48 , 12 * 5 ,12*6 = 72 , 12 * 9 = 108 ( not possible)
12 * 7 = 84 remaining digits 3 , 5 , 6 9 35 + 69 = 104 ( not satisfied)
12 * 8 = 96 ( remaining digits 3 , 4 , 5 , 7 ) not satisfied
13 * 1 , 13 * 2 = 26 , 13 * 3 , 13 * 5 , 13 * 7 = 91 , 13 * 8 = 104 ( not possible)
13 * 4 = 52 remaining digits 6 , 7 , 8 . 9 not satisfied
13 * 6 = 78 remaining digits 2 , 4 , 5 . 9 not satisfied
14 * 1, 14 * 2 = 28 , 14 * 3 = 42 , 14 * 4 , 14 * 5 , 14 * 6 = 84 , ( not possible)
14 * 7 = 98 remaining digits 2 , 3 , 5 . 6 not satisfied
15 , 16 * 1 , 16 * 2 = 32 , 16 * 4 = 64 , 16 * 5 . 16*6 , 16 * 7 = 112 ( not possible)
16 * 3 = 48 remaining digits 2 , 5 , 7 , 9 not satisfied
17 * 1 , 17*3 = 51 , 17 * 5 , 17 * 6 = 102 ( not possible)
17 * 2 = 34 remaining digits 5 , 6 , 8 , 9 not satisfied
17 * 4 = 68 remaining digits 2 , 3 , 5 , 9 (68 + 25 = 93)
we got 1st Solution .
18 * 1 , 18 * 5 , 18 * 6 = 108 ( not possible)
18 * 2 = 36 remaining digits 4 5 , 7 9 not satisfied
18 * 3 = 54 remaining digits 2 6 , 7 9 not satisfied
18 * 4 = 72 remaining digits 3 5 , 6 9 not satisfied 36 + 59 = 95
19 * 1 , 19 * 5 , 19 * 6 = 114 ( not possible)
19 * 2 = 38 remaining digits 4 , 5 , 6 , 7 not satisfied
19 * 3 = 57 remaining digits 2 , 4 , 6 , 8 not satisfied
19 * 4 = 76 remaining digits 2 , 3 , 5 , 8 not satisfied
21 , 22 , 23 * 1 , 23 * 2 , 23 * 3 , 23 * 4 = 94 , 23 * 5 , 23 * 6 = 138 ( not possible)
24* 1 , 24 * 2 , 24 * 3 = 72 , 24 * 4 , 24 * 5 , 25( not possible)
26 * 1 , 26 * 2 , 26 * 4 = 104 ( not possible)
26 * 3 = 78 remaining digits 1 , 4 , 5 , 9 not satisfied
27 * 1 , 27 * 2 , 27 * 4 = 108 ( not possible)
27 * 3 = 81 remaining digits 4 ,5 , 6 , 7 not satisfied
28 * 1 , 28 * 2 , 28 * 3 = 84 ( not possible)
29 * 1 , 29 * 2 , 29 * 4 = 116 ( not possible)
29 * 3 = 87 remaining digits 1 , 4 , 5 , 6
31 , 32 *1 , 32 * 2 , 32 * 3 , 32 * 4 = 128 ( not possible)
33 , 34 * 1 , 34 * 3 , 34 * 4 (136) ( not possible)
35 , 36 * 1 , 36 * 2 = 72 36 * 3 = 108 ( not possible)
37 * 1 , 37 * 2 = 74 , 37 * 3 = 111 ( not possible)
38 * 1 , 38 * 3 = 114 ( not possible)
38 * 2 = 76 remaining digits 1 , 4 , 5 , 9
39 * 1 , 39 * 3 = 117 ( not possible)
39 * 2 = 78 remaining digits 1 , 4 , 5 , 6 ( not satisfied)
41 , 42 * 1 , 42 * 2 , 42 * 3 = 126 ( not possible)
43 * 1 , 43 * 3 = 129 ( not possible)
43 * 2 = 86 remaining digits 1 , 5 , 7 , 9
44 , 45 , 46 * 1 , 46 *2 = 92 , 46 * 3 = 138 (not possible)
47 * 1 , 47 *2 = 94 , 47 * 3 = 141 ( not possible)
48 * 1 , 48 * 3 = 144 not possible
48 * 2 = 96 remaining digits 1 , 3 , 5 , 7
49 * 1 , 49 * 2 = 98 , 49 * 3 = 147 ( not possible)
not further possible as will lead to 3 digit number
17 x 4 = 68 + 25 = 93
Learn more:
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