Race to call 200 with steps of one to eight
Question
Two players alternately call out numbers. The first player opens with any number from to . After that, each call must exceed the previous call by at least and at most . Whoever calls wins. Is there an opening number that guarantees the first player a win with correct play? If so, give it; if not, answer .
Short answer
. Since every turn adds between and , the first player can always restore the running total to a number congruent to , i.e. of the form . Opening with and then answering each move with the next () leaves the opponent unable to stop .
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
Open the worked solutionLessons behind this question
Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.
Read it free