Opening move in a race to fifty
Question
Two players take turns adding a whole number between and (inclusive) to a running total that starts at . Whoever brings the total to exactly wins. You move first. Which number should you open with to guarantee a win?
Short answer
. Whatever your opponent adds, you can reply so the two moves sum to . So the winning totals are those congruent to : . Open with and keep landing on that sequence.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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