AMC / AIME · Base Systems · AIME / USAJMO / AMO

Base Systems: (Proof track.) Give a complete justification. Evaluate math in base ten.

Convert and compute in bases.

Try the problem

**(Proof track.)** Give a complete justification. Evaluate (10101)3(10101)_3 in base ten.

Hint and answer

Concept to use

Digit DP style.

Hint

Expand the numeral as a polynomial in its base and enforce valid-digit constraints.

Answer

91

More Base Systems problems

Practice more with the free Base Systems worksheet generator, or browse the full problem library.