HMMT 2010 U15
- Guts
- Answer
Pick a random integer between 0 and 4095, inclusive. Write it in base 2 (without any leading zeroes). What is the expected number of consecutive digits that are not the same (that is, the expected number of occurrences of either 01 or 10 in the base 2 representation)?
Dataset text NuminaMath olympiads. Quoted with source.
Show the answer
\frac{20481}{4096}
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Similar problems
These problems have the most words in common with this statement.