How many numbers less than 1000 DO NOT have a 7 as a digit?

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1

<p>A friend says it's 719, but I get 728, and we don't have the answer booklet. Please help.</p>

2

<p>I believe the answer is 729 , because first digit has to be 0 , second digit has 9 posibilties, third has 9, and fourth also has 9, so 9^3 = 729</p>

3

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<p>Sorry I forgot to mentioned that the question asked for the number of positive numbers less than 1000. </p>

<p>BTW, are you sure that you method works for problems like this one? I did it the long way by counting. 999-(19*5)-100.</p>

4

<p>I’m getting 728…</p>

<p>It can have 1, 2 or 3 digits.</p>

<p>If it has 1 digit, there are 8 possibilites (1 thru 9, minus 7)</p>

<p>If it has two digits, there are 72 of them (8 choices for the tens, 9 for the ones, multiply).</p>

<p>If there are 3 digits, there are 648 of them (8 choices for the hundreds, 9 for the tens, 9 for the ones).</p>

<p>Add 'em up.</p>

5

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/834400-number-range-manipulation-problems.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/834400-number-range-manipulation-problems.html&lt;/a&gt;&lt;/p&gt;

<p>The question was:</p>

<p>Example from the 2009 PSAT:</p>

<p>How many positive integers less than 1,000 do not have 7 as any digit?
(A) 700
(B) 728
(C) 736
(D) 770
(E) 819</p>

<p>Note how ETS was kind enough NOT to list 729. :)</p>

6

<p>When looking at the solutions posted in the link above, please remember that positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5. </p>

<p>The last post might be misleading.</p>

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<p>Zero is an integer, but is neither positive nor negative.</p>

7

<p>Got it guys! Thanks. So it’s 728. </p>

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<p>Thanks for the link.</p>