No. LXXIV.—IN THE TRAIN
The Puzzle Problem—
A passenger in a first-class railway carriage notices that the top of a factory window due S.W. of him coincides with a mark on the carriage window, and does not move from it while the train is running five and a half miles.
At the end of that distance the compass bearing of the chimney is due N.W. How far was the passenger from the chimney when he first noticed it?
is solved by 31⁄2 miles.
We give a diagram to make the points clear.
As the chimney top does not move from its place on the window, it is clear that the train is running on a segment of a circle having the chimney for its centre. It follows that the observer’s distance throughout is equal to the radius of that circle, and the radius of a circle of which the quadrant measures 51⁄2 miles is 31⁄2 miles within about 11 ft.