Problems(1)
Adam, Bendeguz, Cathy, and Dennis all see a positive integer n. Adam says, "n leaves a remainder of 2 when divided by 3." Bendeguz says, "For some k, n is the sum of the first k positive integers." Cathy says, "Let s be the largest perfect square that is less than 2n. Then 2nās=20." Dennis says, "For some m, if I have m marbles, there are n ways to choose two of them." If exactly one of them is lying, what is n?