A group of n students are numbered continously from first sdtudent as 1,2,3,...... If 1101 digits had to be used in all,what is the number of students in the group


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Question Number 55482 by pooja24 last updated on 25/Feb/19

$A g r o u p o f n s t u d e n t s a r e n u m b e r e d$ $c o n t i n o u s l y f r o m f i r s t s d t u d e n t a s 1, 2, 3, . . . . . .$ $I f 1101 d i g i t s h a d t o b e u s e d i n a l l, w h a t i s t h e$ $n u m b e r o f s t u d e n t s i n t h e g r o u p$
	Answered by mr W last updated on 25/Feb/19

	$1, 2, 3 . . ., 9 \Rightarrow Σ = 9 \times 1 = 9 d i g i t s$ $10, 11, 12, . . ., 99 \Rightarrow Σ = 90 \times 2 = 180 d i g i t s$ $100, 101, 102, . . ., 999 \Rightarrow Σ = 900 \times 3 = 2700 d i g i t s$ $s i n c e t o t a l l y 1101 d i g i t s a r e u s e d,$ $n m u s t b e a 3 - d i g i t n u m b e r$ $9 + 180 + (n - 99) \times 3 = 1101$ $\Rightarrow n = 403$ $i . e . t h e r e a r e 403 s t u d e n t s i n t h e g r o u p .$
	Commented by tanmay.chaudhury50@gmail.com last updated on 25/Feb/19

	$e x c e l l e n t s i r . . .$
	Commented by mr W last updated on 25/Feb/19

	$t h a n k s s i r!$ $i f m = f (n) i s t h e t o t a l n u m b e r o f d i g i t s$ $f r o m 1 t o n . i s i t p o s s i b l e t o f i n d a$ $f o r m u l a f o r f (n) i n t e r m s o f n ?$ $f u r t h e r m o r e f i n d n = f^{- 1} (m) i f$ $p o s s i b l e .$
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