Question 629158: Imagine that you have a set of integers e.g. {1, 2, 3, 4, 5, 6}.
In how many ways can we form groups of size 1,2,...6, by taking into account that we only can group consecative numbers (and of course single).
For example, some examples are:
1) {1} {2} {3} {4} {5} {6} (6 groups)
2) {1,2} {3,4} {5,6} (3 groups)
3) {1} {2,3} {4,5} {6} (4 groups)
4) {1,2,3,4,5,6} (1 group)
and so on.....
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Think of this string:
A1B2C3D4E5F6G
We must choose a left bracket "{" to go where the A is. That's 1 way.
We may either choose "} {" or a comma "," to go where the B is. That's 2 ways.
We may either choose "} {" or a comma "," to go where the C is. That's 2 ways.
We may either choose "} {" or a comma "," to go where the D is. That's 2 ways.
We may either choose "} {" or a comma "," to go where the E is. That's 2 ways.
We may either choose "} {" or a comma "," to go where the F is. That's 2 ways.
We must choose a right bracket "}" to go where the G is. That's 1 way.
Answer: 1 = 32 ways.
Edwin
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