ROSECODE 126
Flip-flop Bit Sets
Let B be the binary digits of an integer N
B = { b1, b2, b3, ..., bn } b1 is the least significant bit and bn = 1
Consider the subsets of B whose elements are alternately 0 and 1
Example: N = 40, B = { 0, 0, 0, 1, 0, 1 }
There are 11 such flip-flop subsets (including the empty set):
How many flip-flop subsets are there for N = 1234567891011121314?
[My timing: < 100ms]
B = { b1, b2, b3, ..., bn } b1 is the least significant bit and bn = 1
Consider the subsets of B whose elements are alternately 0 and 1
Example: N = 40, B = { 0, 0, 0, 1, 0, 1 }
There are 11 such flip-flop subsets (including the empty set):
| Index | Values |
|---|---|
| [] | {} |
| [1, 4] | {0, 1} |
| [1, 6] | {0, 1} |
| [2, 4] | {0, 1} |
| [2, 6] | {0, 1} |
| [3, 4] | {0, 1} |
| [3, 6] | {0, 1} |
| [5, 6] | {0, 1} |
| [1, 4, 5, 6] | {0, 1, 0, 1} |
| [2, 4, 5, 6] | {0, 1, 0, 1} |
| [3, 4, 5, 6] | {0, 1, 0, 1} |
[My timing: < 100ms]