document.write( "Question 1164864: Hello. I am stuck with this question and have no idea how to start it. Here it is:
\n" ); document.write( "A palindromic number is one which reads the same backwards as forwards.
\n" ); document.write( "(a) Find a three-digit palindromic number which is exactly 19 times the
\n" ); document.write( "sum of its digits.
\n" ); document.write( "(b) Find all four-digit palindromic numbers which are exactly 352 times
\n" ); document.write( "the sum of their digits.
\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #789334 by MathTherapy(10552) $\"\"$ $\"About$

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Hello. I am stuck with this question and have no idea how to start it. Here it is:
\n" ); document.write( "A palindromic number is one which reads the same backwards as forwards.
\n" ); document.write( "(a) Find a three-digit palindromic number which is exactly 19 times the
\n" ); document.write( "sum of its digits.
\n" ); document.write( "(b) Find all four-digit palindromic numbers which are exactly 352 times
\n" ); document.write( "the sum of their digits.
\n" ); document.write( "Thanks!
\n" ); document.write( "

(a)  A 3-digit palindrome will have the same hundreds and units digits
\n" );
document.write( "     Let hundreds/units and tens digits be H, and M, respectively
\n" );
document.write( "     Then the number is: 100H + 10M + H
\n" );
document.write( "     Since the number is 19 times the sum of its digits, we get: 100H + 10M + H = 19(H + M + H)
\n" );
document.write( "     101H + 10M = 19(2H + M)
\n" );
document.write( "     101H + 10M = 38H + 19M
\n" );
document.write( "     101H - 38H = 19M - 10M
\n" );
document.write( "     63H = 9M =====> 
\n" );
document.write( "     M is a DIGIT, so H, or hundreds/units digit can ONLY be 1. Therefore, M = 7(1) = 7
\n" );
document.write( "    \r
\n" );
document.write( "\n" );
document.write( "(b)  A 4-digit palindrome will have the same thousands and units digits, and the same hundreds and tens digits
\n" );
document.write( "     Let thousands/units and hundreds/tens digits be T, and H, respectively
\n" );
document.write( "     Then the number is: 1,000T + 100H + 10H + T, or 1,001T + 110H
\n" );
document.write( "     Since the number is 352 times the sum of its digits, we get: 1,001T + 110H = 352(T + H + H + T) 
\n" );
document.write( "     1,001T + 110H = 352(2T + 2H)
\n" );
document.write( "     1,001T + 110H = 704T + 704H
\n" );
document.write( "     1,001T - 704T = 704H - 110H
\n" );
document.write( "     297T = 594H =====> 
\n" );
document.write( "     H is a DIGIT, and can ONLY be 1, 2, 3, or 4. Therefore:   \n" );
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