3consider the set x = { 1 , 2 , 3 , 4 , 5 } and suppose you have two holes. also suppose that you have 10 pigeons: the 2 -element subsets of x . can you put these 10 pigeons into the two holes in a way that there is no 3 -element subset s = { a , b , c } ⊂ x for which all pigeons from s go in the same hole? then answer the same question if x = { 1 , 2 , 3 , 4 , 5 , 6 } with 15 = c ( 6 , 2 ) pigeons.

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