For a positive integer n > 2, consider the n-1 fractions
2/1; 3/2; ...; n/(n-1).
The product of these fractions equals n, but if you reciprocate (i.e. turn upside down) some of the fractions, the
product will change.
How can you make the product equal 1?
Find all values of n for which this is possible.
Jack has challenged you to play a card game with him. The idea of the game is that a player gets a random card and after seeing it it's placed back in the deck. The player may get as many cards as he/she wants and the sum of the values of these cards represents the points this player got. However if the player gets an ace he/she gets zero points as total and the other player may try. How should one play this game (how many cards should be picked) for maximum chance of winning against Jack?
Face cards can be interpreted so that king is 13 points, queen is 12 points and jack is 11 points.