36 (number)
36 (thirty-six) is the natural number following 35 and preceding 37. In mathematics. 36 is both the square of six and a triangular number, making it a square triangular number. It is the smallest square triangular number other than one, and it is also the only triangular number other than one whose square root is also a triangular number. It is the smallest number "n" with exactly eight solutions to the equation φ("x") = "n". It is the smallest number with exactly nine divisors, leading 36 to be a highly composite number. Adding up some subsets of  its divisors (e.g., 6, 12, and 18) gives 36, hence it is a semiperfect number. This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers. 36 is the number of degrees in the interior angle of each tip of a regular pentagram. The thirty-six officers problem is a mathematical puzzle with no solution. The number of possible outcomes (not summed) in the roll of two distinct dice. 36 is the largest numeric base that some computer systems support because it exhausts the  numerals, 0–9, and the letters, A-Z. See Base 36. The truncated cube and the truncated octahedron are Archimedean solids with 36 edges. The number of domino tilings of a 4×4 checkerboard is 36. Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. The sum of the integers from 1 to 36 is 666 (see number of the beast).