What is the smallest positive four-digit integer that is the product of two consecutive integers?
I want to find two consecutive integers, x and x + 1, such that x(x + 1) is a four-digit number. That means x(x + 1) must be at least 1000, the smallest four-digit number. So I need to find the smallest value of x that satisfies this inequality. I can try some values of x and see when the inequality holds. If x = 10, then x(x + 1) = 10 * 11 = 110, which is too small. If x = 20, then x(x + 1) = 20 * 21 = 420, which is still too small. If x = 30, then x(x + 1) = 30 * 31 = 930, which is getting closer but not enough. If x = 31, then x(x + 1) = 31 * 32 = 992, which is also too small. If x = 32, then x(x + 1) = 32 * 33 = 1056, which is the first four-digit product I get. So x = 32 and x + 1 = 33 are the two consecutive integers I'm looking for. The smallest positive four-digit integer that is the product of two consecutive integers is 1056. 