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-

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, \dots \dots

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 \dots, 9 \Rightarrow Σ = 9 \times 1 = 9 d i g i t s

10, 11, 12, \dots, 99 \Rightarrow Σ = 90 \times 2 = 180 d i g i t s

100, 101, 102, \dots, 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 \dots

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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