Twelve basketball players, whose uniforms are numbered 1 through 12, stand around the center ring on the court in an arbitrary arrangement. Show that some three consecutive players have the sum of their numbers at least 20.

Answer:ShownStep-by-step explanation:Given that twelve basketball players, whose uniforms are numbered 1 through 12, stand around the center ring on the court in an arbitrary arrangement. Let us consider consecutive numbers in this set.[tex]1+2+3 =6<20\\2+3+4 =9<20\\3+4 +5=12<20\\...\\\\5+6+7=18<20[/tex]After this we find the totals are more than 20.When 1 to 12 are arbitrarily arranged, there are chances that numbers from 6 and above are having consecutive numbers.These totals are greater than 20Hence shown that some three consecutive players have the sum of their numbers at least 20.(i.e. starting from if we take)