Reconstruction

The school decided to carry out a renovation and began by replacing the doors. After installing the doors, the principal decided to number each door. As soon as he had this idea, he had the mathematicians calculate how many individual digits were needed if the doors were numbered starting from 1. They found that 318 digits were needed. How many doors are there in the school?

Final Answer:

n =  142

Step-by-step explanation:

n1=9 n2=2 (9910+1)=180 n3=3 (999100+1)=2700  318n1n2=3 (n100+1) 3189180=3 (n100+1)  3n=426  n=3426=142  n=142   Verifying Solution:  N3=3 (n100+1)=3 (142100+1)=129 s=n1+n2+N3=9+180+129=318



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