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UW Math Hour Olympiad 2014 Grades 8-10 #5

Source:

June 2, 2014
modular arithmeticMath Hour Olympiad

Problem Statement

An infinite number of lilypads grow in a line, numbered \dots, 2-2, 1-1, 00, 11, 22, \dots Thumbelina and her pet frog start on one of the lilypads. She wants to make a sequence of jumps that will end on either pad 00 or pad 9696. On each jump, Thumbelina tells her frog the distance (number of pads) to leap, but the frog chooses whether to jump left or right. From which starting pads can she always get to pad 00 or pad 9696, regardless of her frog's decisions?