Pick the right subset.
Consider the set of the first 'n' natural numbers i.e. {1,2,3,4,5,6........,n}. Let us denote this set by [n].
Now, let us define another function R=R(n), such that
R(n)= the minimum number of elements I should choose from [n] so that among the chosen elements there always exists X, Y , Z such that X + Y = Z
Find R(6).
The answer is 5.
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1 solution
I solved it on using a trial and error strategy. So if -
i) R(6) is 1, which cannot be true.
ii) R(6) is 2, cannot be true because my chosen set can be {1,3}
iii) R(6) is 3, cannot be true because my chosen set can be {1,3,6}
iv) R(6) is 4, cannot be true because my chosen set can be {3,4,5,6}
So it has to be R(6) = 5. This is because no matter which 5 elements I choose there always exist numbers like X, Y, Z.
For instance, if my chosen set is {1,2,3,5,6} then I have 1 + 2 = 3