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Question Number 41754 by Tawa1 last updated on 12/Aug/18

	Answered by candre last updated on 12/Aug/18

	$we have from 1 to 1000 number that can have 3$ $3 \times \times$ $\times 3 \times$ $\times \times 3$ $separating cases$ $\times \times 3 :$ $10 \times 10 = 100 (9 \times 9 = 81)$ $\times 3 \times :$ $10 \times 10 = 100 (9 \times 9 = 81)$ $3 \times \times :$ $10 \times 10 = 100 (9 \times 9 = 81)$ $analysying the intersection$ $\times 33 : 10 (9)$ $3 \times 3 : 10 (9)$ $33 \times : 10 (9)$ $333 : 1$ $so, b y i n c l u s i o n e x c l u s i o n p r i n c i p e$ $100 + 100 + 100 - 10 - 10 - 10 + 1 = 271$ $or, counting alredy excluding overlaping (() one)$ $81 \times 3 + 9 \times 3 + 1 = 271$
	Commented by Tawa1 last updated on 12/Aug/18

	$God bless you sir$
	Answered by tanmay.chaudhury50@gmail.com last updated on 12/Aug/18

	$1) s i n g l e d i g i t n u m b e r u s i n g 3 i s = 1$ $2) t w o d i g i t n u m b e r u n i t p l a c e i s 3 t h e n t e n g t h$ $p l a c e c a n b e f i l l e d b y u s i n g (1, 2, 3, 4, 5, 6, 7, 8, 9)$ $9 w a y s s o = 9$ $3) t w o d i g i t n u m b e r t e n g t h p l a c e i s 3 t h e n u n i t$ $p l a c e c a n b e (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) = 10$ $4) t h r e e d i g i t n u m b e r h u n d r e d p l a c e i s 3$ $t e n t h p l a c e (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) 10 w a s$ $s i m i l a r l y u n i t p l a c e 10 w a y s = 1 \times 10 \times 10 = 100$ $5) t h r e e d i g i t n u m b e r t e n g t h p l a c e i s 3$ $h u n d r e d p l a c e (1, 2, 3, 4, 5, 6, 7, 8, 9) = 9 w a y s$ $u n i t p l a c e (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) = 10 w a y s$ $1 \times 9 \times 10 = 90$ $6) t h r e e d i g i t n u m b e r u n i t p l a c e i s 3$ $t e n g t h p l a c e (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)$ $h u n d r e d p l a c e (1, \bar{2} 3, \bar{} 4, 5, 6, 7, 8, 9)$ $1 \times 10 \times 9 = 90$ $s o t o t a l = 1 + 9 + 10 + 100 + 90 + 90 = 300$
	Commented by Tawa1 last updated on 12/Aug/18

	$God bless you sir$
	Answered by MrW3 last updated on 12/Aug/18

	$3 : \Rightarrow 1$ $3 X : \Rightarrow 9$ $X 3 : \Rightarrow 8$ $33 : \Rightarrow 1 \times 2 = 2$ $Σ = 19$ $3 X Y : \Rightarrow 9 \times 9 = 81$ $X 3 Y : \Rightarrow 8 \times 9 = 72$ $X Y 3 : \Rightarrow 8 \times 9 = 72$ $33 X : \Rightarrow 2 \times 9 = 18$ $3 X 3 : \Rightarrow 2 \times 9 = 18$ $X 33 : \Rightarrow 2 \times 8 = 16$ $333 : \Rightarrow 1 \times 3 = 3$ $Σ = 280$ $\Rightarrow 1 + 19 + 280 = 300$
	Commented by Tawa1 last updated on 12/Aug/18

	$God bless you sir$
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