In how many no. between 100 and 1000 at least one of their digits is 7?
Pick one.
A) 900 B) 648 C) 720 D) 252 E) 729
Let's count the number of occurrences with only one 7:   (1) 7XX:  1 * 9 * 9= 
<gadget id="calculator"> 1 * 9 * 9</gadget>
<output>81</output>
81   (2) X7X: 8 * 1 * 9= 
<gadget id="calculator">8 * 1 * 9</gadget>
<output>72</output>
72   (3) XX7: 8 * 9 * 1= 72   81 + 72 + 72= 
<gadget id="calculator">81 + 72 + 72</gadget>
<output>225</output>
225   At this point we can already see that the answer must be D since the choice are very dispersed.   Anyways, let's count number of occurrences with two 7s:   (1) 77X: 1 * 1 * 9= 
<gadget id="calculator">1 * 1 * 9</gadget>
<output>9</output>
9   (2) X77: 8 * 1 * 1= 8   (3) 7X7: 1 * 9 * 1 = 9   9 + 8 + 9= 
<gadget id="calculator">9 + 8 + 9</gadget>
<output>26</output>
26   Number 777 is missing. So the total becomes   225 + 26 + 1= 
<gadget id="calculator">225 + 26 + 1</gadget>
<output>252</output>
252   252 is the correct answer.
<result>D</result>
In how many no. between 100 and 1000 at least one of their digits is 7?