document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141460>Question 1141460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My child has been given this question in homework.\r<BR>\n" );
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document.write( "I am thinking of a 3 digit number<BR>\n" );
document.write( "When it is divided by 9, the remainder is 3<BR>\n" );
document.write( "When it is divided by 2, the remainder is 1<BR>\n" );
document.write( "When it is divided by 5, the remainder is 4<BR>\n" );
document.write( "What is my number? </SPAN>\n" );
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document.write( "(1) divided by 5 leaves remainder 4 --> last digit is either 4 or 9<br><BR>\n" );
document.write( "(2) divided by 2 leaves remainder 1 --> last digit is odd<br><BR>\n" );
document.write( "From (1) and (2), the last digit is 9.<br><BR>\n" );
document.write( "That much is fairly basic and can be understood by fairly young children.  The last part is more advanced.<br><BR>\n" );
document.write( "A number is divisible by 9 if, and only if, the sum of the digits is a multiple of 9.  As a corollary to that, a number will leave a remainder of 3 when divided by 9 if, and only if, the sum of the digits is 3 more than a multiple of 9.<br><BR>\n" );
document.write( "So with last digit 9, the sum of the other two digits has to be 3 more than a multiple of 9 -- i.e., either 3 or 12.  Fortunately there are many 3-digit numbers that satisfy these conditions.<br><BR>\n" );
document.write( "Sum of other two digits = 3: 129, 219, 309.<BR>\n" );
document.write( "Sum of other two digits = 12: 399, 489, ... 939.<br><BR>\n" );
document.write( "The way the problem is presented, it sounds as if there is supposed to be a single answer.  Clearly there are multiple possible answers if the number is 3 digits.<br><BR>\n" );
document.write( "There would only be a single answer if the number were 2 digits. Is it possible that that is what the problem is supposed to be? </SPAN>\n" );
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