Let M a positive integer is called “Minos” if in its binary representation, any two consecutive appearance of digit 1 are separated by 2 or more 0. Example 36= 100100 (binary) is “Minos” number, but 37=100101 not.
How many nonnegative integers that can be represented as binary sequence of length 20 (leading zeros allowed) are ‘Minos’?
My tough:
C=# of ceros N=# of ones T=# total
*) Two ceros always must be together, when are all 0 . In this case the number 0 is Minos.
*) Now 1 one and 19 ceros 20 different numbers.
*) Now 2 ones and 18 ceros then 20Cn2 In conclusion I’m thinking the solution will be all the sum of all the combination of numbers taken in group of 2.
Note: Regarding my answer, I posted because something doesn’t sound quite right, and I cannot see how can I proceed to calculate the correct answer, and how lead into it. Thanks.