document.write( "Question 1011714: there are 3 judges, judging a sporting event. Each of these judges holds up a number, either 1 or a 2 or a 3. The sum of these numbers is the athletes's score.how many different scores are possible? \n" ); document.write( "
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\n" ); document.write( "Question:
\n" ); document.write( "There are 3 judges, judging a sporting event. Each of these judges holds up a number, either 1 or a 2 or a 3. The sum of these numbers is the athletes's score.how many different scores are possible?
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\n" ); document.write( "Solution:
\n" ); document.write( "The minimum score is 1+1+1=3
\n" ); document.write( "The maximum score is 3+3+3=9
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\n" ); document.write( "We need to examine if all numbers in-between are possible:
\n" ); document.write( "At the start, if all judges give a score of one, the total score is 3.
\n" ); document.write( "If each judge changes her mind and increase the score by one, we get 4,5,and 6.
\n" ); document.write( "The same process can be repeated to get 7,8,9.
\n" ); document.write( "So the total possible number of scores is (9-3)+1=7\r
\n" ); document.write( "\n" ); document.write( "following added to clarify answer:
\n" ); document.write( "The set of possible scores is {3,4,5,6,7,8,9} which gives 7 distinct scores.\r
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