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==Example==
Example 1:# The set {{math|1=''S'' = {{mset| 20, 23, 25, 30, 49, 45, 27, 30, 30, 40, 22, 19 }}}} can be partitioned into the four sets {{math|{{mset| 20, 25, 45 }}, {{mset| 23, 27, 40 }}, {{mset| 49, 22, 19 }} , {{mset| 30, 30, 30}}}}, each of which sums to ''T'' = 90.
Example 2:# The set {{math|1=''S'' = { {mset|1, 2, 5, 6, 7, 9 }}}} can be partitioned into the two sets { {math|{{mset|1, 5, 9 }}, { {mset|2, 6, 7 }}}} each of which sum to ''T'' = 15. ▼
Example 3# (every integer in ''S'' is strictly between ''T''/4 and ''T''/2): {{math|1=''S'' = { {mset|4,5,5,5,5,6 }}}}, thus ''m''=2, and ''T''=15. There is feasible 3-partition { {math|{{mset|4,5,6 }}, { {mset|5,5,5 }}}}. ▼▲Example 2: The set ''S'' = {1, 2, 5, 6, 7, 9} can be partitioned into the two sets {1, 5, 9}, {2, 6, 7} each of which sum to ''T'' = 15.
Example 4# (every integer in ''S'' is strictly between ''T''/4 and ''T''/2): {{math|1=''S'' = { {mset|4,4,4,6,6,6 }}}}, thus ''m''=2, and ''T''=15. There is no feasible solution. ▼
▲Example 3 (every integer in ''S'' is strictly between ''T''/4 and ''T''/2): ''S'' = {4,5,5,5,5,6}, thus ''m''=2, and ''T''=15. There is feasible 3-partition {4,5,6}, {5,5,5}.
▲Example 4 (every integer in ''S'' is strictly between ''T''/4 and ''T''/2): ''S'' = {4,4,4,6,6,6}, thus ''m''=2, and ''T''=15. There is no feasible solution.
==Strong NP-completeness==
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