Number theory · Parity · Pairwise sums · Counting · Extremal problems
Let \(x\), \(y\), \(z\) and \(w\) be natural numbers. At most how many of the six sums
\[ x+y, \quad x+z, \quad x+w, \quad y+z, \quad y+w, \quad z+w \]
can be odd?
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
- E \(6\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2022, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source