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You can put this solution on YOUR website!
The problem is not well defined; I can't see any interpretation that gives 6 different numbers between 1 and 10 that can be written in the prescribed form.\r
\n" ); document.write( "\n" ); document.write( "(1) I assume by \"numbers\" you mean whole numbers.
\n" ); document.write( "(2) Does \"between 1 and 10\" include both 1 and 10? or neither?
\n" ); document.write( "(3) What are the restrictions on m and n?\r
\n" ); document.write( "\n" ); document.write( "If m and n must be positive integers, then the answer is less than 6.\r
\n" ); document.write( "\n" ); document.write( "If m and n can be either positive integers or 0, then every number between 1 and 10 except 1 can be written in the prescribed form.\r
\n" ); document.write( "\n" ); document.write( "If m and n can also be negative integers, then every integer can be written in the prescribed form.
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\n" ); document.write( "I am new to this web site; so I don't know the right way to respond to your message.... So I'm adding it to my original response.
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\n" ); document.write( "Nobody can help you find the answer until you provide a precise description of the problem. You have said that 1 and 10 do not count; that clears up one ambiguity. Presumably we are looking at whole numbers, so we are considering 2, 3, 4, 5, 6, 7, 8, and 9.
\n" ); document.write( "Your statement of the problem says we are to find the sum of the 6 numbers in this group that can be expressed as 3m+2n -- but you say nothing about what values m and n can have.
\n" ); document.write( "Again I assume m and n can have only integer values; otherwise clearly any number can be expressed in the form 3m+2n.
\n" ); document.write( "And if m and n can be negative integers, than any integer can be expressed in the form 3m+2n.
\n" ); document.write( "So there seem to be only two possibilities: (1) m and n have to be positive integers, or 0; or (2) m and n have to be positive integers.
\n" ); document.write( "But neither of these interpretations gives 6 numbers between 1 and 10 that can be written in the form 3m+2n.
\n" ); document.write( "If m and/or n can be 0, then we have
\n" ); document.write( "2 = 3(0)+2(1)
\n" ); document.write( "3 = 3(1)+2(0)
\n" ); document.write( "4 = 3(0)+2(2)
\n" ); document.write( "5 = 3(1)+2(1)
\n" ); document.write( "6 = 3(2)+2(0) or 3(0)+2(3)
\n" ); document.write( "7 = 3(1)+2(2)
\n" ); document.write( "8 = 3(2)+2(1) or 3(0)+2(4)
\n" ); document.write( "9 = 3(3)+2(0) or 3(1)+2(3)
\n" ); document.write( "So all 8 of the numbers between 1 and 10 can be written in the required form.
\n" ); document.write( "If neither m nor n can be 0, then we have
\n" ); document.write( "5 = 3(1)+2(1)
\n" ); document.write( "7 = 3(1)+2(2)
\n" ); document.write( "8 = 3(2)+2(1)
\n" ); document.write( "9 = 3(1)+2(3)
\n" ); document.write( "And in this case only 4 numbers can be written in the required form.
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\n" ); document.write( "So again I say, no interpretation of the problem I can see will give us 6 of the 8 numbers being able to be expressed as 3m+2n.
\n" ); document.write( "If you want help with this, you need to make sure you are stating the problem correctly, including saying what values m and n can have. \n" ); document.write( "