hobbit wrote:

even 19 is not enough....

you can still get 9 odd and 10 even...

however, i think the question is not wroded carefully...

when you say you draw n cards... do you mean that the n cards drawn have an even sum, or do you mean that UNTIL the Nth card drawn you get at an even sum on the way (i.e. maybe the (n-1) first cards or (n-2) first cards have even sum)...

if you simply draw n cards and expect to get an even sum - then you must draw ALL 20 cards.below that you can always come with a combination of odd number of odd cards and whatever number of even cards to complete it.

You are correct, hobbit. I thought of it while having lunch. You must have all the cards (that is 20) drawn to get an even sum.