document.write( "Question 713948: Your bank requires you to pick a four digit PIN for your debit card from the digits 0-9. How many different PINs are possible if adjacent digits cannot be the same? (For example the PIN 1123 would be invalid but 1213 would not.) \n" ); document.write( "
Algebra.Com's Answer #438635 by Edwin P McCravy(4)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First let's count all possible types of unacceptable PINs, and then\r\n" );
document.write( "count the number in each type\r\n" );
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document.write( "There are 3 types of unacceptable PINs which use exactly 3 different digits\r\n" );
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document.write( "AABC, for instance 7792\r\n" );
document.write( "ABBC, for instance 4885\r\n" );
document.write( "ABCC, for instance 6099\r\n" );
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document.write( "Those account for 10·9·8 each or 3·10·9·8 = 2160\r\n" );
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document.write( "There are 6 types which use exactly 2 different digits\r\n" );
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document.write( "AAAB, for instance 5551\r\n" );
document.write( "AABA, for instance 3373\r\n" );
document.write( "ABAA, for instance 5355\r\n" );
document.write( "BAAA, for instance 7333\r\n" );
document.write( "AABB, for instance 6611\r\n" );
document.write( "ABBA, for instance 2882\r\n" );
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document.write( "Those account for 10·9 each or 6·10·9 = 540\r\n" );
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document.write( "There is only 1 type that uses exactly 1 digit.\r\n" );
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document.write( "AAAA, for instance 7777\r\n" );
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document.write( "There are 10 of those.\r\n" );
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document.write( "So we have a grand total of 2160+540+10 = 2710 unacceptable PINs\r\n" );
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document.write( "There are 10·10·10·10 or 10000 4 digit PINs with no restrictions.\r\n" );
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document.write( "So there are 10000-2710 or 7290 acceptable PINs.\r\n" );
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document.write( "Answer: 7290\r\n" );
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document.write( "Edwin
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