I need help to solve these problems :
1. A dartboard is divided into 6 sections. These 6 sections is given numbers : 49, 5, 54, 28, 37, 23. What is the least number of throws needed in order to get a score of exactly 100?
I have noticed that a sum of 100 can be from the sum of 3 numbers : 23+23+54, 49+28+23. But I have no idea how to work it out.
2. In a party, there are 2006 cakes. The first group eats 1/2 of them. The second group eats 1/3 of the rest. The third group eats 1/4 of the rest. An so on .... The 2005th group eats 1/2006 of the rest. How many cakes have been eaten ?