0, 1 Repel
Level
pending
Find the number of 7-digit ternary strings that do not have any 0's next to any 1's. 00200211 and 00211200 are 2 strings to be counted, while 00200120 is a string not to be counted.
(A ternary string is a string consisting of only 0's, 1's, and 2's.)
The answer is 577.
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1 solution
Let x y represent the number of y-digit ternary strings that ends with x . We find these recursive equations: 0 n + 1 = 0 n + 2 n , 1 n + 1 = 1 n + 2 n , 2 n + 1 = 0 n + 1 n + 2 n .
We know that 0 1 = 1 1 = 2 1 = 1 , and we can find the answer: 0 7 + 1 7 + 2 7 = 1 6 9 + 1 6 9 + 1 6 9 = 5 7 7 .