MathDB

Patchouli is taking an exam with

k > 1

parts, numbered Part

1, 2, \dots, k

. It is known that for

i = 1, 2, \dots, k

, Part

i

contains

i

multiple choice questions, each of which has

(i+1)

answer choices. It is known that if she guesses randomly on every single question, the probability that she gets exactly one question correct is equal to

2018

times the probability that she gets no questions correct. Compute the number of questions that are on the exam.
Proposed by Yannick Yao

Problem Statement