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* Anyone? | * Anyone? | ||
What I've found most confusing is knowing when to subtract repetitions of things, like in problem 44 on the homework, where we're asked to find how many strings there are with five consecutive 0s or five consecutive 1s. What's a good method for knowing or deciding how to count something like that? | What I've found most confusing is knowing when to subtract repetitions of things, like in problem 44 on the homework, where we're asked to find how many strings there are with five consecutive 0s or five consecutive 1s. What's a good method for knowing or deciding how to count something like that? | ||
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| + | The goal is to count each thing exactly once. Counting everything a certain number of times is almost as good, as you can just divide by that number. | ||
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| + | If you know how many times individual elements were counted, that is the next best thing. You count how many elements of that type exist, and divide by that number. For example, you may have counted everything with 7 ones like 1111111000, 0111111100 and 1011111110 (and so on) 3 times (for 3 different sets of '11111'), and thus just count these separately and divide by 3. | ||
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| + | What may be less work than this is just to devise a method that actually only counts '''exactly''' once instead of a different number of times. It may take a little more thought, but I think it's worth it in the end. | ||
Revision as of 10:43, 10 September 2008
- Anyone?
What I've found most confusing is knowing when to subtract repetitions of things, like in problem 44 on the homework, where we're asked to find how many strings there are with five consecutive 0s or five consecutive 1s. What's a good method for knowing or deciding how to count something like that?
The goal is to count each thing exactly once. Counting everything a certain number of times is almost as good, as you can just divide by that number.
If you know how many times individual elements were counted, that is the next best thing. You count how many elements of that type exist, and divide by that number. For example, you may have counted everything with 7 ones like 1111111000, 0111111100 and 1011111110 (and so on) 3 times (for 3 different sets of '11111'), and thus just count these separately and divide by 3.
What may be less work than this is just to devise a method that actually only counts exactly once instead of a different number of times. It may take a little more thought, but I think it's worth it in the end.
