SOLUTION: Lockers are numbered with consecutive positive integers beginning with 1, and the digit 2 is used exactly 106 times (including on the last locker). What is the number of the last l

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Question 1121426: Lockers are numbered with consecutive positive integers beginning with 1, and the digit 2 is used exactly 106 times (including on the last locker). What is the number of the last locker?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
There are 20 in the first 100, 2,12,22,32...,92 (11)and 20-29, excluding 22 (9)
There are 20 from 101-199
Need 66 more:
200-219 (22)
220-229 (21)
230-249 (22)
250 ANSWER

Answer by ikleyn(52872)   (Show Source): You can put this solution on YOUR website!
. 
1-9     (2 used  1 time - 105 to go) 
10-19   (2 used  1 time - 104 to go) 
20-29   (2 used 11 times - 93 to go) 
30-99   (2 used  7 times - 86 to go) 
100-119 (2 used  2 times - 84 to go) 
120-129 (2 used 11 times - 73 to go) 
130-199 (2 used  7 times - 66 to go) 
200-219 (2 used 22 times - 44 to go) 
220-229 (2 used 21 times - 23 to go) 
230-239 (2 used 11 times - 12 to go) 
240-249 (2 used 11 times -  1 to go) 
250     (2 used  1 time  -  0 to go)


250 is your answer (the brute-force way)

Similar way of solution you may find at the link

https://answers.yahoo.com/question/index?qid=20150521162733AATuEl2

https://answers.yahoo.com/question/index?qid=20150521162733AATuEl2

But that solution contains numerous ERRORS (actually, fatal errors) that I fixed in my post.



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