You have all the clubs from a deck, 13 cards, and you can choose 2 from the deck and get paid their product, where all face cards are considered to be 0. You can pay $1 to reveal the difference of any two cards you choose, how much would you pay to play this game?

Answer:$11.Step-by-step explanation:As the question states,Number of clubs from the deck = 13Number of selections which can be made = 2Amount we are paid is the product of the cards value.Value of Face Card = 0Amount paid to reveal the difference of any two cards = $1So,The Maximum amount one person can get is when he get 9 and 10 as the value.So,Maximum Win = 9 x 10 = $90For this,We know we can guarantee the $90 total when we get the cards 9 and 10.For this there are two cases:Case 1 : 10 cards with some value and 3 cards with 0 value. Starting with one card from the Face valued cards.Here, we will be left with only 2 zeroes.The maximum we can pay 10 + 1 = $11 to know that in maximum 11 steps we came to know the number 9 and 10.Case 2 : 10 cards with some value and 3 cards with 0 value. Starting with the cards other than Face Value cards.Here, we will be left with 3 zeroes.Therefore, in maximum 11 tries we can find out the required product of 90.By paying $11.Total Win $90 and Money Spent = $11. Therefore we can get $90 by paying atleast $11.