Question Number 18498 by Tinkutara last updated on 22/Jul/17

Commented by richard last updated on 23/Jul/17

Answered by Abbas-Nahi last updated on 23/Jul/17

Answered by richard last updated on 23/Jul/17

Commented by mrW1 last updated on 23/Jul/17

Commented by richard last updated on 23/Jul/17

Commented by richard last updated on 23/Jul/17

Commented by richard last updated on 23/Jul/17

Commented by richard last updated on 23/Jul/17

Commented by mrW1 last updated on 23/Jul/17

Commented by Abbas-Nahi last updated on 23/Jul/17

Commented by richard last updated on 23/Jul/17

Answered by richard last updated on 22/Jul/17

Answered by Abbas-Nahi last updated on 23/Jul/17

Answered by mrW1 last updated on 24/Jul/17
![N=number of numbers in which zero(s) occurs Z=number of zero(s) in the numbers X∈[1,9] Y∈[1,3] W∈[1,2] (1) numbers with 1 digit: X N=0 Z=0 (2) numbers with 2 digits: X0 N=9 Z=9 (3) numbers with 3 digits: (3.1) X0X, XX0 N=2×9×9=162 Z=162 (3.2) X00 N=9 Z=9×2=18 (4) numbers with 4 digits: (4.1) W0XX, WX0X, WXX0 N=3×2×9×9=486 Z=486 (4.2) W00X, W0X0, WX00 N=3×2×9=54 Z=54×2=108 (4.3) W000 N=2 Z=2×3=6 (4.4) 30XX, 3Y0X, 3WX0, 33Y0 N=9×9+3×9+2×9+3=129 Z=129 (4.5) 300X, 3Y00, 30X0 N=9+3+9=21 Z=21×2=42 (4.6) 3000 N=1 Z=3 ΣN=9+162+9+486+54+2+129+21+1=873 ΣZ=9+162+18+486+108+6+129+42+3=963 i.e. there are 873 numbers in which “0” occurs. in them “0” is written 963 times.](https://www.tinkutara.com/question/Q18560.png)
Commented by Tinkutara last updated on 24/Jul/17

Commented by mrW1 last updated on 24/Jul/17
