The number of times the digit 3 will be written when listing the integers from 1 to 1000 is


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Question Number 48543 by Pk1167156@gmail.com last updated on 25/Nov/18

$The number of times the digit 3 will$ $be written when listing the integers$ $from 1 to 1000 is$
	Answered by mr W last updated on 25/Nov/18

	$o n e - d i g i t - n u m b e r s :$ $3 \Rightarrow 1 n u m b e r \Rightarrow 1 t i m e$ $t w o - d i g i t - n u m b e r s :$ $x 3 \Rightarrow 8 n u m b e r s \Rightarrow 8 t i m e s$ $3 x \Rightarrow 9 n u m b e r s \Rightarrow 9 t i m e s$ $33 \Rightarrow 1 n u m b e r \Rightarrow 2 t i m e s$ $t h r e e - d i g i t - n u m b e r s :$ $x y 3 \Rightarrow 8 \times 9 = 72 n u m b e r s \Rightarrow 72 t i m e s$ $x 3 y \Rightarrow 8 \times 9 = 72 n u m b e r s \Rightarrow 72 t i m e s$ $3 x y \Rightarrow 9 \times 9 = 81 n u m b e r s \Rightarrow 81 t i m e s$ $x 33 \Rightarrow 8 n u m b e r s \Rightarrow 16 t i m e s$ $33 x \Rightarrow 9 n u m b e r s \Rightarrow 18 t i m e s$ $3 x 3 \Rightarrow 9 n u m b e r s \Rightarrow 18 t i m e s$ $333 \Rightarrow 1 n u m b e r s \Rightarrow 3 t i m e s$ $Σ t i m e s = 1 + 8 + 9 + 2 + 72 + 72 + 81 + 16 + 18 + 18 + 3$ $Σ t i m e s = 300$
	Answered by mr W last updated on 27/Nov/18

	$3 x y : 10 \times 10 = 100 t i m e s$ $x 3 y : 9 \times 10 = 90 t i m e s$ $3 y : 10 t i m e s$ $x y 3 : 9 \times 10 = 90 t i m e s$ $x 3 : 9 t i m e s$ $3 : 1 t i m e$ $Σ t i m e s = 100 + 100 + 100 = 300$
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