Sum=110
Probability
Level
3
Let . How many elements must we select from S to ensure that there will be at least two distinct integers among them whose sum is 110.
The answer is 15.
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1 solution
Partition set S into { 3 } , { 5 5 } , { 7 , 1 0 3 } , { 1 1 , 9 9 } , . . . , { 5 1 , 5 9 } . It is not enough to select 14 elements, as we can select exactly one element from each partition and no two of them add up to 110. 15 elements are sufficient , as at least one of the 2-element-partition has all of its elements being chosen and they add up to 110.