document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189473>Question 1189473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A,B, and C are distinct digits, and 8•AB=ACA . Find the product of A•B•C </SPAN>\n" );
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document.write( "8 times \"AB\" is equal to \"ACA\".<br><BR>\n" );
document.write( "Since 8 is even, the last digit of the product, A, must be even.<br><BR>\n" );
document.write( "So the possibilities are<BR>\n" );
document.write( "8*(2B)=2C2<BR>\n" );
document.write( "8*(4B)=4C4<BR>\n" );
document.write( "8*(6B)=6C6<BR>\n" );
document.write( "8*(8B)=8C8<br><BR>\n" );
document.write( "The only one of those that has any possible solutions is the first.  So A is 2. (8 times 4B is at most 8*49<400; and similarly for A=6 or A=8....)<br><BR>\n" );
document.write( "So 8*(2B)=2C2; and the product 8*(2B) is at least 8*20=160 and at most 8*29=232.<br><BR>\n" );
document.write( "Finally, 8*29=232 is the only multiple of 8 greater than 200 and less than or equal to 232 that has units digit 2.  So 8*29=232 is the solution to the given multiplication problem.<br><BR>\n" );
document.write( "ANSWER: A*B*C=2*9*3=54<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );