#190: The Hikers' Surprise

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Answer to #189: The cells 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 will be open. Only the cells that have two of the same factors (4 = 2 * 2) will be open because they are opened and closed the same number of times (except 1 which is just opened). Since they have the same factor twice their number of factors is odd.
(Dedicated to BooBooKitty_)

Four hikers are forced into a cabin with no lights by a bad storm. On the door of the cabin is a sign that reads, "Come in as you please, but fall asleep and you will die." Being very superstitious, they all take this very seriously and devise a plan so they can all stay awake. They all stand in a corner and one person walks from one corner along the wall to the next and taps the person in that corner making sure they are awake. They do this for many hours until one hiker suddenly runs out of the cabin screaming along with all of the others. Why did they run out terrified? [Slide for answer]

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