Question

A deck of 14cards numbered from 1through 14 is dealt to Ken and Gunther so that each gets 7 cards. Each player's score is the sum of card values and the player with lower score wins. How many different winning scores be are possible?

Answer 1

the different winning scores possible are 25 (from 28 to 52).

Explanation:

the minimum score obtained by a player will be 28.

• since, we divide 1-7 numbered to one and 8-14 to the other player such that one receives the maximum and the other receives the minimum.

the least minimum possibility is :28 as one get the card as(1,2,3,4,5,6,7).

• for increasing this score now we give the number 1,2,3,4,5,6,8 to one of the player so that they sum upto 29 and will get the minimum score and wins.

• next possible minimum sum to win will be 30 by assigning 1,2,3,4,5,6,9.

continuing in the same way we see that the minimum sum obtained to win will be 52( by assigning 2,3,6,7,9,12,13).

Hence, there are total 25 winning scores possible.