A string of n left and n right brackets is said to be balanced if each right bracket has a matching preceding left bracket and each left bracket has a matching subsequent right bracket. Here is a balanced string of 4 left and 4 right brackets: () ( () () )
How many different balanced strings can one form with 4 left and 4 right brackets?
i managed to count 13 possibilities?
can anyone confirm this, or are there more??
thanks in advance!
2007-12-07 11:38:34 · 2 answers · asked by PeterW 1 in Science & Mathematics ➔ Mathematics
Perhaps 14?
+ = left bracket
- = right bracket
+ + + + - - - -
+ + + - + - - -
+ + + - - + - -
+ + + - - - + -
+ + - + + - - -
+ + - + - + - -
+ + - + - - + -
+ + - - + + - -
+ + - - + - + -
+ - + + + - - -
+ - + + - + - -
+ - + + - - + -
+ - + - + + - -
+ - + - + - + -
2007-12-07 14:14:20 · answer #1 · answered by oregfiu 7 · 1⤊ 0⤋
nicely, 3x+a million>10 -a million -a million 3x > 9 So divide 3 from the two components. 3 divided by utilising 3x equals 1x which equals x. Then 9 divided by utilising 3, which equals 3 so... x>3 So in case you plug in 10 back into the unique equation. 3(10)+a million>10 provided that's larger than the value of x aka 3. you multiply thrice 10 and get 30 and upload a million 31. So, 31 is larger than 10 so it works. all of it sounds confusing however the answer is x>3.
2016-12-10 15:56:47 · answer #2 · answered by Anonymous · 0⤊ 0⤋