# GeekDad Puzzle of the Week: Geek Kids in Prison – Solution

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BadDad may care a great deal about the kids touching his stuff, but he is generally lax when it comes to dangerous equipment. Xerxes,
Yervant, and Zed were playing with the cool wormhole generator BadDad brought home recently and suddenly found themselves facing a hostile reception on an alien planet. Now they are in prison and must get out as soon as possible before the generator loses its charge.

The prison is surrounded by a courtyard and outer wall.
Heavily-armed guards stand duty. Using their keen powers of observation, the kids have devised a plan to escape through the window of their cell and over the outer wall at X.

There are two guards outside the outer wall. One starts at A1, 500
yards west of a point outside their window, marches 550 yards to A2, 50
yards east of a point outside their window, and turns about. The last guard starts at B1 (same point as A2), marches 500 yards east to B2 and turns about.

There are also two guards inside the outer wall. One starts at C1,
300 yards west of a point outside their window, marches to C2 outside their window, and turns about. Another starts at D1 outside their window and marches to D2, 400 yards to the east and turns about.

The guards start from points A1, B1, C1, and D1, and march up and down their watch at a regular speed of 100 yards per minute (no need to include turning time).

The kids can only hope to escape unseen if they do it in the dark, one kid at a time, as long as each kid has a clear two minutes with all the guards at least 100 yards away. It is dark enough for their attempt at 9:00 p.m. by their Earth watch. At that time, new guards come on duty.

At what time should Xerxes, Yervant, and Zed escape?

Solution
Find the range of times at which the guards starting from A1, B1, C1, and D1 are out of range (more than 100 yards away).

Xerxes, Yervant, and Zed find the first three periods of two minutes or more that are common to all of these ranges. They are:

9:10:30 until 9:14
9:34 until 9:37
9:41 until 9:44

They slip out unnoticed, jump back to Earth, and BadDad is none the wiser.

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