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Question Number 50732 by hassentimol last updated on 19/Dec/18

	Answered by Rasheed.Sindhi last updated on 19/Dec/18

	$(10 a + b) \times c = 10 d + e$ $(10 d + e) + (10 f + g) = 10 h + i$ $∙ c {c a n}^{'} t b e 1 b e c a u s e i n t h a t c a s e$ $a = d & b = e$ $∙ 12 ⩽ 10 a + b ⩽ 49 (b / c c i s a t l e a s t 2)$ $C o n t i n u e$
	Commented by hassentimol last updated on 19/Dec/18

	$Thank you Sir . God bless you .$
	Commented by hassentimol last updated on 19/Dec/18

	$But it is impossible to resolve . . .$ $There is too much unknown and only$ $2 equations . . . ?$
	Answered by Rasheed.Sindhi last updated on 20/Dec/18

	$1 7$ $\times 4$ $- - - -$ $6 8$ $+ 2 5$ $- - - -$ $9 3$
	Commented by ajfour last updated on 20/Dec/18

	$E x c e l l e n t S i r, a n y m e t h o d ?$
	Commented by Rasheed.Sindhi last updated on 20/Dec/18

	$T h a n k s f o r e n c o u r a g i n g S i r!$ $T h e m e t h o d i s a m i x t u r e o f i n t e l l i g e n t$ $g u e s s i n g & t r i a l .$
	Answered by MJS last updated on 21/Dec/18

	$a b \times c = d e$ $b, c \neq 1 otherwise e = b \lor e = c \Rightarrow c ⩾ 2$ $d e < 100 \land c ⩾ 2 \Rightarrow a ⩽ 4$ $b, c \neq 5 otherwise e = 5 \lor e = 0$ $(b, c) \notin {(2, 6), (4, 6), (6, 2), (6, 4), (6, 8), (8, 6)}$ $which combinations fit ?$ $c = 2 \land a = 1 \Rightarrow b \in {7, 8, 9}$ $c = 2 \land a = 3 \Rightarrow b \in {4, 8, 9}$ $c = 2 \land a = 4 \Rightarrow b \in {3, 8}$ $c = 3 \land a = 1 \Rightarrow b \in {6, 8, 9}$ $c = 3 \land a = 2 \Rightarrow b \in {6, 7, 9}$ $c = 4 \land a = 1 \Rightarrow b \in {3, 7, 8, 9}$ $c = 6 \land a = 1 \Rightarrow b = 3$ $c = 7 \land a = 1 \Rightarrow b \in {2, 4}$ $c = 8 \land a = 1 \Rightarrow b = 2$ $so we have :$ $(1) listed c \times d e = f g$ $(2) wrote down left digits in {}$ $(3) ‘ ‘ X^{″} sorted out because no possibility to add$ $a 2 digit number and stay < 100$ $(4) testing the matches for d e + f g = h i$ $2 \times 17 = 34 {5, 6, 8, 9} 34 + f 5 = h 9 X$ $2 \times 18 = 36 {4, 5, 7, 9} 36 + f 9 = h 5 X$ $2 \times 19 = 38 {4, 5, 6, 7} 38 + f 6 = h 4 X 38 + f 7 = h 5 X$ $2 \times 34 = 68 {1, 5, 7, 9} 68 + f 1 = g 9 X 68 + f 7 = h 5 X 68 + f 9 = h 7 X$ $2 \times 38 = 76 {1, 4, 5, 9} 76 + f 5 = h 1 X 76 + f 9 = h 5 X$ $2 \times 39 = 78 {1, 4, 5, 6} 78 + f 6 = h 4 X$ $2 \times 43 = 86 {1, 5, 7, 9} X$ $2 \times 48 = 96 {1, 3, 5, 7} X$ $3 \times 16 = 48 {2, 5, 7, 9} 48 + f 7 = h 5 X 48 + f 9 = h 7 X$ $3 \times 18 = 54 {2, 6, 7, 9} 54 + f 2 = h 6 X$ $3 \times 19 = 57 {2, 4, 6, 8} X$ $3 \times 26 = 78 {1, 4, 5, 9} 78 + f 1 = h 9 X$ $3 \times 27 = 81 {4, 5, 6, 9} X$ $3 \times 29 = 87 {1, 4, 5, 6} X$ $4 \times 13 = 52 {6, 7, 8, 9} X$ $4 \times 17 = 68 {2, 3, 5, 9} 68 + f 5 = h 3 \Rightarrow 68 + 25 = 93$ $4 \times 18 = 72 {3, 5, 6, 9} X$ $4 \times 19 = 76 {2, 3, 5, 8} 76 + f 2 = h 8 X$ $6 \times 13 = 78 {2, 4, 5, 9} X$ $7 \times 12 = 84 {3, 5, 6, 9} X$ $7 \times 14 = 98 {2, 3, 5, 6} X$ $8 \times 12 = 96 {3, 4, 5, 7} X$
	Commented by Rasheed.Sindhi last updated on 03/Feb/19

	$G o o D s t r a t e g y! B e t t e r t h a n m i n e .$
	Commented by hassentimol last updated on 24/Dec/18

	$Thank you sir, amazing!$
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