Consider the set A = {1, 4, 7, 10, 13, 16___97, 100}. All subsets of A having N elements have the property that there are two elements in the set whose sum is 104. Find the minimum value of N.
Answers
Step-by-step explanation:
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Given : A = {1, 4, 7, 10, 13, 16___97, 100}.
All subsets of A having N elements have the property that there are two elements in the set whose sum is 104.
To Find : Value of N
Solution:
A = {1, 4, 7, 10, 13, 16___97, 100}
form is 3n+ 1 where n is integer from 0 to 33
Let say two element are 3p+1 , 3q+1 where p , q ∈ n
3p+1 + 3q + 1 = 104
3(p + q) = 102
=> p + q = 34
p = 1 , q = 33 ( 4 , 100)
p = 2 q = 32 (7 , 97)
p = 15 q = 19 ( 46 , 58)
p = 16 q = 18 ( 49 , 55)
Hence there are 16 sets having the property that there are two elements in the set whose sum is 104
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