Math interview questions

Convert a number's string representation between any two bases from 2 to 36 — parse the digits in the source base, then re-emit them in the target base.

Add and multiply arbitrarily large non-negative integers given as decimal strings, using digit-by-digit schoolbook arithmetic with carries.

Convert between Excel column titles and numbers in both directions — A is 1, Z is 26, AA is 27 — the classic bijective base-26 system with no zero digit.

Raise a base to an integer exponent in logarithmic time using exponentiation by squaring, handling negative exponents.

Compute the greatest common divisor with Euclid's algorithm and the least common multiple, for two numbers or a whole list.

Compute the integer square root — the floor of the real square root — using Newton's method, without Math.sqrt.

Test whether a number is prime and generate all primes up to n with the Sieve of Eratosthenes.

Convert between Roman numerals and integers in both directions, handling subtractive notation like IV, IX, and XL.

Round, floor, and ceil a number to N decimal places without the classic floating-point drift — 1.005 must round to 1.01, not 1.00.

Reimplement JavaScript's parseInt — skip leading whitespace, read an optional sign and radix prefix, consume valid digits for the base, and stop at the first invalid character.

Pick items at random in proportion to their weights using prefix sums and a binary search, with an injectable RNG so picks are testable.

Spell out a non-negative integer in English words — break it into groups of three digits and name each group with its scale word.