Problema Solution
A wall is covered with balloons. Each balloon has the number 5, 3 or 2 printed on it . You are given 7 darts to throw at the wall . If your dart breaks a ballon , the you earn the number of points printed on the balloon . If your dart does not break a balloon , then you are awarded 0 points for that shot. You win a prize if your total is exactly 16 points on seven shots. If your total is over 16 or under ,then you lose. Determine the number of different point combinations that can be used to win the game.
Answer provided by our tutors
16 prime factors to 2^4
5 is a prime number
3 is a prime number
2 is a prime number
so all possibilities have to involve factors of '2' in some manner
6: one each of 5 and 3 combined with four 2s
7: two 3s and five 2s
6: four 3s and two 2s
5: two 5s and three 2s
4: two each of 5 and 3
there are only five point combinations on hits to win the game