<p>Did I mention that this is one of my favorite topics in math? Here's another one to play with:</p>
<p>How many positive 4-digit integers have at least one repeated digit? (The repeated digits do not have to be consecutive: 1223 and 1232 would both qualify.)</p>
<p>This is beyond me. How is it done?</p>
<p>Im also wondering how</p>
<p>Sent from my MB855 using CC App</p>
<p>Is the answer 900?</p>
<p>Sent from my MB855 using CC App</p>
<p>Is it… 4464?..
I’m not entirely sure.</p>
<p>Can you tell me where my approach might be flawed?
There are 9000 possible 4 digit positive integers.
I found out there are 9<em>9</em>8*7 integers have no repeating digits.</p>
<p>9000-(9<em>9</em>8*7) = 4464 possible integers with at least one repeated digit.</p>
<p>This might be wrong… I’m not really good at math…</p>
<p>^ Shouldn’t it be 9 x 8 x 7 x 6 for no repeating digits?</p>
<p>
</p>
<p>It would be 9 * 9 * 8 * 7 because 0 can be used after the first digit.</p>
<p>Aren’t there 9999 positive 4 digit integers?</p>
<p>Sent from my MB855 using CC App</p>
<p>
</p>
<p>I believe there are 9999 positive integers. (1-9999)
There are 9000 positive four digit integers. (1000-9999)
Simple mistake… haha</p>
<p>Nvm realized you have to subtract the 999 </p>
<p>Sent from my MB855 using CC App</p>
<p>There are 9999 numbers with 4 digits OR FEWER!</p>
<p>And I think JeffJung has it right… 
</p>
<p>BTW, I think this problem is pretty nasty even though it uses only the counting principle. Also think it is too hard to be on an SAT!</p>
<p>Not too hard, but hard enough to be number 20. ;)</p>
<p>Nice find though, I’m sure it’ll help in the exam.</p>
<p>
I agree. However, I have seen some problems on the SAT where I cannot find a solution without applying at least a pre-calc level math. (Maybe my school’s algebra class just sucked.)
In that regard, I can picture this problem on the SAT…</p>
<p>^Maybe a #20. But I felt as I was writing this question that I was putting in too many twists for it to be truly SAT-like. After all, if it stumped some of YOU guys… :)</p>
<p>SAT Math is too hard… It’s too tricky…</p>