Math Is Fun Forum

How do I do it?

Like sin 90 = 1 and sin 210 = -1

Is there a chart that list the values and the only way for me is to memorize them?

Or is there some kind of pattern I can follow?

The doughnut shop has 5 kinds of doughnuts: a, b, c,d and e. There are unlimited supply of each kind. In how many ways can you order a dozen doughnuts?

Well, my first instict is to simply 5^12. But then I realize aaaab is the same as baaaa... hence the order doesnt matter.

I'm trying to do it by cases:

Case 1: one daughnuts only.

(5 C 1) x 1 = 5 ways

Case 2: two daughnuts only.

(5 C 2) x 13 = 130
But this include one daughnuts, so its 130-5 = 125.

The problem starts here. I dont know why the arrangements for 2 daughnuts is 13. I got it by simply listing out all the cases.

Then I tried using simpler problems, like let's say you want to buy 5 daughnuts out of 3 different daughnuts. I can find out the number of ways for this one, but I see no relation if let's say you want to buy 6 daughnuts.

I sat down for 2 hours and still couldnt figure it out

My last bet is 13^4... but that's a wild guess. Help is appreciated.

1. Ten trees - four pines, four cedars, and two spruce- are planted in two parallel rows of five trees. How many arrangements are possible if each row must have the same composition of trees, not necessarily in the same order.

2. Suppose we want to creat subsets of the ten digits {0, 1, 2, ...., 9}
  a) How many subsets can be created, including the empty set?
  b) How many of the subsets contain only digits less than 7?
  c) How many of the subsets contain 0 or 9?

Find the largest value of k so that 10^k divides evenly into 100!

To be honest, I dont really understand what the quesiton is asking. Help is appreciated!

1) Prove that no square integer number can have a remainder of 3 when divided by 5

2) A school has 1000 students, and their lockers, which are numbered from 1 to 1000, are all closed, The first student opens all the lockers. The second student closes every second locker, beginning with her locker #2. The third student CHANGES the state of every third locker, beginning with locker #3, which means a locked locker becomes open and an open locker becomes closed. This carries on until all 1000 students had their turn.

Which lockers are open and why?

After some work, I think the locker with perfect square numbers are open. So locker #1, 4, 9, 16, 25 etc are open. But I dont know how to prove this and it might not work for numbers within 900-1000.

Also, I need help solving the first problem in this thread :

http://www.mathsisfun.com/forum/viewtopic.php?id=2859