In the diagram of rooms and connecting doorways below, can you draw a path that crosses every doorway exactly once?
Know the answer? Send your solution to ar@casact.org.
The Length of Days and Nights
In this puzzle, at location A when the date is halfway between the Spring Equinox and the Summer Solstice the day is about 14 hours long. About how long will the night be at A during the Summer Solstice (the Puzzle Date)? What about during the Winter Solstice?
- Note 1: Published length of day is from www.timeanddate.com/sun. When the event occurs late in the evening or early in the morning (UTC time), I use the average of the two bracketing dates.
- Note 2: See later discussion (see AR Online) of my misestimation of the length of day on the Puzzle Day, which I suspect is driven by my approximation of a perfectly circular orbit around the sun, rather than the actual elliptical orbit.
Bob Conger submitted an extremely detailed solution treatise. The short version follows below.
Solutions were also sent in from John Berglund, Sean Porreca and David Zheng.
Results
- The earth’s axis tilts 17.041 degrees towards the sun on the Puzzle Date (compared with 0 degrees towards the sun on the spring equinox and 23.436 degrees towards the sun on the summer solstice). Further discussion of this element later. (See full solution.)
- Location A is positioned at latitude 38.067 degrees N or S, any longitude, a result that is directly dependent on the angle of the axis, above.
