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Printjmc
number theory junior
Problem
If the pattern shown continues, what is the letter in the th position? MATHLETEMATHLETEMATHLETE...
Solution
The pattern repeats with every 8 letters, so we can determine the letter in the th position by finding the remainder when is divided by 8. We can check that 2008 is a multiple of 8. That means 2010 has a remainder of 2 when divided by 8. The letter in the th position will be the same as the letter in the second position of the pattern, which is .
Final answer
A