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Nine stones are arranged in a straight line. They are counted from left to right as \($1,2,3, \ldots, 9$\), and then from right to left, so that the stone previously counted as 8 is counted as 10. The pattern is continued to the left until the stone previously counted as 1 is counted as 17. The pattern then reverses so that the stone originally counted as 2 is counted as 18, 3 as 19, and so on. The counting continues in this manner. Which of the original stones is counted as 99? Express your answer as a single digit which corresponds to the first digit assigned to that stone.

 Nov 30, 2020
 #1
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The stone that is counted as 99 is stone 1.

 Nov 30, 2020
 #2
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The pattern repeats every 8 counts. Therefore:

 

99 mod 8 =3 - the 99th count should land on 3.

 Nov 30, 2020
 #3
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3 is correct

 Nov 30, 2020

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