Understand the problem
Source of the problem
Austrian-polish mathematical Olympiad 1978
Start with hints
Prove that the element found in hint 2 is common to all the sets.
Let be a set such that . Consider the sets . They are all singleton sets and they are pairwise distinct (prove it!). This means that has more than 50 elements, which is a contradiction.
Connected Program at Cheenta
Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.