A jailer in a prison with infinitely many cells decides to release some of the prisoners. The jailer first unlocks the doors of all the cells. Next he reverses the locks on the door of every second cell (cell numbers 2, 4, 6,...); so, the even numbered cells are now locked again. Next he reverses the locks on the door of every third cell (cell numbers 3, 6, 9,...). Cell 3 was unlocked and is now reversed back to locked. Cell 6, however, had last been locked; so, it is now reversed back to unlocked. Next the jailer reverses the locks on the doors of every fourth cell, then every fifth cell,.... The process continues without end. Which cells will remain unlocked? [Problem submitted by Ron Kendis, LACC Professor of Mathematics.] |
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SOLUTION |

| Problem 1 | Problem 2 | Problem 3 | Problem 4 | Problem 5 |

| Problem 6 | Problem 7 | Problem 8 | Problem 9 | Problem 10 |