How many chickens?

Your father gives you $100 to go to town and buy 100 chickens, the prices are as follows:

• $1 for a Hen
• $5 for a Rooster
• $.5 for a Chick

You have to buy at least one of each kind of chicken, what are the numbers of each kind of chicken you need?

Solution:


Well, I kinda cheated to get the answer. I wrote a Qbasic program to figure all the permutations that work. I did optimizes it, I went though the Chicks in steps of 2 (to get rid of the decimal). I also only went up to 20 Hens because at that point you are already out of money. But other then that I just did the equivalent of smashing the circle block in to the square slot with a hammer.

1. 1 Rooster
   91 Hens
   8 Chicks
   
   
2. 2 Roosters
   82 Hens
   16 Chicks
   
   
3. 3 Roosters
   73 Hens
   24 Chicks
   
   
4. 4 Roosters
   64 Hens
   32 Chicks
   
   
5. 5 Roosters
   55 Hens
   40 Chicks
   
   
6. 6 Roosters
   46 Hens
   48 Chicks
   
   
7. 7 Roosters
   37 Hens
   56 Chicks
   
   
8. 8 Roosters
   28 Hens
   64 Chicks
   
   
9. 9 Roosters
   19 Hens
   72 Chicks
   
   
10. 10 Roosters
    10 Hens
    80 Chicks
    
    
11. 11 Roosters
    1 Hen
    88 Chicks