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document.write( "(1) a+b+c=9\r\n" );
document.write( "(2) d+e+f+i=26\r\n" );
document.write( "(3) i+f+g+h=21\r\n" );
document.write( "(4) h+g+c=11\r\n" );
document.write( "(5) b+c+e+f+g=30 \r\n" );
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document.write( "We know that\r\n" );
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document.write( " 1+2+3+4+5+6+7+8+9 = 45\r\n" );
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document.write( "So therefore we know that\r\n" );
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document.write( "(6) a+b+c+d+e+f+g+h+i = 45\r\n" );
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document.write( "Add equations (1) and (2) \r\n" );
document.write( "(1) a+b+c = 9\r\n" );
document.write( "(2) +d+e+f+i = 26 \r\n" );
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document.write( "(7) a+b+c+d+e+f+i = 35\r\n" );
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document.write( "Subtract equation (7) from equation (6)\r\n" );
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document.write( "(6) a+b+c+d+e+f+g+h+i = 45\r\n" );
document.write( "(7) a+b+c+d+e+f +i = 35\r\n" );
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document.write( "(8) g+h = 10\r\n" );
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document.write( "Subtract (8) from (4), swapping\r\n" );
document.write( "h and g in (8) \r\n" );
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document.write( "(4) h+g+c = 11\r\n" );
document.write( "(8) h+g = 10\r\n" );
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document.write( " c = 1\r\n" );
document.write( "Substitute in (5)\r\n" );
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document.write( "(5) b+c+e+f+g = 30\r\n" );
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document.write( " b+1+e+f+g = 30\r\n" );
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document.write( "(9) b+e+f+g = 29 \r\n" );
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document.write( "From (9), those four digits b,e,f, and g have to be large to add to 29, so if\r\n" );
document.write( "they were as large as they could be, 9,8,7,6, their sum would be 9+8+7+6=30,\r\n" );
document.write( "just 1 more than 29. And the only way we can make that sum 1 smaller is to\r\n" );
document.write( "replace the 6 by a 5, and have 9+8+7+5=29. But we don't yet know which letter\r\n" );
document.write( "equals which number. However we know that these two sets are equal:\r\n" );
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document.write( "(10) {b,e,f,g} = {9,8,7,5}\r\n" );
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document.write( "We already have c=1, so the set of the remaining four letters has to equal the\r\n" );
document.write( "set of the remaining 4 numbers. So\r\n" );
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document.write( "(11) {a,d,h,i} = {2,3,4,6}\r\n" );
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document.write( "Put those together so we can look at them:\r\n" );
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document.write( "(11) {a,d,h,i} = {2,3,4,6}\r\n" );
document.write( "(10) {b,e,f,g} = {9,8,7,5}\r\n" );
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document.write( "Now look at (1)\r\n" );
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document.write( "(1) a+b+c=9\r\n" );
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document.write( "We already have c=1, so substituting,\r\n" );
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document.write( "(1) a+b+1=9\r\n" );
document.write( "(1) a+b=8\r\n" );
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document.write( "So a and b must have sum 8. Look back at (11) and (10). 'a' must come from (11)\r\n" );
document.write( "and 'b' must come from (10). So the only way that can be is for 'a' to equal 3\r\n" );
document.write( "and 'b' to equal 5, for no other pair adds to 8.\r\n" );
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document.write( "So far we have a=3, b=5, c=1\r\n" );
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document.write( "Now the sets in (10) and (11) become\r\n" );
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document.write( "(11) {d,h,i} = {2,4,6}\r\n" );
document.write( "(10) {e,f,g} = {9,8,7}\r\n" );
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document.write( "Now we look at (8)\r\n" );
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document.write( "(8) g+h = 10\r\n" );
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document.write( "'g' must come from (10) and 'h' must come from (11). So the only way that can\r\n" );
document.write( "be is for 'g' to equal 8 and 'h' to equal 2, for no other pair adds to 10.\r\n" );
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document.write( "Now so far we have \r\n" );
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document.write( "a=3, b=5, c=1, g=8, h=2,\r\n" );
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document.write( "Now (11) and (10) become:\r\n" );
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document.write( "(11) {d,i} = {4,6}\r\n" );
document.write( "(10) {e,f} = {9,7}\r\n" );
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document.write( "We look at (3)\r\n" );
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document.write( "(3) i+f+g+h=21. Substituting g=8 and h=2,\r\n" );
document.write( " i+f+8+2=21\r\n" );
document.write( " i+f+10=21\r\n" );
document.write( " i+f=11\r\n" );
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document.write( "'i' must come from (11) and 'f' must come from (10). So the only way that can\r\n" );
document.write( "be is for 'i' to equal 4 and 'f' to equal 7, for no other pair adds to 11.\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "a=3, b=5, c=1, g=8, h=2, i=4, f=7\r\n" );
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document.write( "Now (11) and (10) become:\r\n" );
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document.write( "(11) {d} = {6}\r\n" );
document.write( "(10) {e} = {9}\r\n" );
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document.write( "So d=6 and e=9.\r\n" );
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document.write( "So the solution is:\r\n" );
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document.write( "a=3, b=5, c=1, d=6, e=9, f=7, g=8, h=2, i=4\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "a+b+c = 9\r\n" );
document.write( "3+5+1 = 9\r\n" );
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document.write( "d+e+f+i = 26\r\n" );
document.write( "6+9+7+4 = 26\r\n" );
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document.write( "i+f+g+h = 21\r\n" );
document.write( "4+7+8+2 = 21\r\n" );
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document.write( "h+g+c = 11\r\n" );
document.write( "2+8+1 = 11\r\n" );
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document.write( "b+c+e+f+g = 30\r\n" );
document.write( "5+1+9+7+8 = 30\r\n" );
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document.write( "Edwin \n" );
document.write( "