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first take out 7 & 77 & 777 ---> total of six sevens.

next step is to think about x7 or 7x ---> x can be either 1,2,3 ... so for x7 you have 8 ways (excluding 0,7) and for 7x you have 9 ways (excluding 7).

now we have xx7 and x7x ---> every one of them has 72 ways , 8 for the first x and 9 for the second x ---> 8*9 = 72 (excluding 0,7 for the first x and 7 for the second x)

next 7xx ---> 9 ways * 9 ways = 81 (excluding only 7).

and last we have x77 or 77x and 7x7 --> 8 ways, 9 ways, and 9 ways ---> don't forget you get two sevens so multiply by two !!!

thanks so much for the detailed explanation killer. the question is quite a handful, but ur explanation clarifies it very well. i appreciate it man. : )

how many times will the digit 7 be written when listing the integers from 1 to 1000?

110 111 271 300 304

again any replies i would really appreciate it. this question is giving me this huge headache...lol.

From 1-100 There are 7,17,27,47,57,67,87,97 So multiply this by 10
=90
From 71-79 There are 10 7's (counting 77) = 9*10=90

We are discounting the 700-799 so far.
So total now is 180.

Now counting 700-799. we have 799-700+1=100 #'s. However this doenst cover all of the 7's just yet.

Now consider: 707,717,727,737,747,757,767,787,797 = 9 additional 7's on the end.

Now from 770-779. we have 770,771,772,773,774,775,776,777,778,779. we have 11 7's b/c we have an additional 7 from 777.

so 180+9+11+100=300!

Ans. D.

I don't really see a quick way to solve this. Just gotta know all the possibilities that 7 can show up.

My original answer was actually 301. So come test day i dunno if i would have picked 304 or 300. Not bad to narrow down to 2 answers, but considering i spent bout 3min on the prob. thats no good.

My approach for such types of questions, which needs count of particular digit in first thousand numbers.

Count the number of digits appearing in 100
7 will appear 20 times in writing first 100 numbers.
In 1000 numbers, total number of digits = 20*100 + 100 (701...800)= 300