Problem:
The wheel shown is spun twice, and the randomly determined numbers opposite the pointer are recorded. The first number is divided by , and the second number is divided by . The first remainder designates a column, and the second remainder designates a row on the checkerboard shown. What is the probability that the pair of numbers designates a shaded square?
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Answer Choices:
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Solution:
The first remainder is even with probability and odd with probability . The second remainder is even with probability and odd with probability . The shaded squares are those that indicate that both remainders are odd or both are even. Hence the square is shaded with probability
The problems on this page are the property of the MAA's American Mathematics Competitions