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Start with 10,000 quarters, all “heads up” and lined up in a (long) row. Number each quarter starting from the left and working to the right (1st, 2nd, 3rd, etc…). Then carry out the following procedure:
Step 1: Turn over every quarter
Step 2: Turn over every second quarter (2nd, 4th, 6th, etc…)
Step 3: Turn over every third quarter (3rd, 6th, 9th, etc…)
$\vdots$
Step 10,000: Turn over the ten-thousandth quarter
So in general, in Step $n$, turn over every quarter that is in a position that is a multiple of $n$.
At the end of Step 10,000, which coins will be heads up and which will be tails up?