Let [tex]M[/tex] = {1, 2, ..., 2048}, and [tex]X \subset M[/tex] such that [tex]\left| X \right| = 15 [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Show that there are two distinct subsets of [tex]X[/tex] whose sum of elements is the same.

ie.

[tex]A,B \subset X[/tex] and [tex]A \cap B = \oslash[/tex]

[tex]\sum_{\substack{a\in A}}a[/tex] = [tex]\sum_{\substack{b\in B}}b[/tex]

Does this have something to do with the fact that 2^11=2048?

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# Difficlut problem

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