2016 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 1

Problem

Suppose there are $9$ lights arranged on tic-tac-toe board so that one is in each square. Suppose further that there are six light switches one for each row and column. Flipping any of these switches turns on all lights that are off and turns off all lights that are in the column/row controlled by this switch. If there is exactly one light on, can you turn all the lights on using the given switches? As in all problems you need to explain your answer.

Solution

See also

2016 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
First question
Followed by
Problem 2
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All UNM-PNM Problems and Solutions

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