There are three measures of distance in the land of irrationalia- the mile, the dist (1+√2 miles), and the ance (1+1/√2 miles).

Measured from the beginning of a proposed new highway, the Dist Auto mobile club have proposed to put an emergency telephone every dist. The Ance Automobile club have similarly proposed the same, but to every ance.

Also, measured from the beginning of the highway, there will be a milestone every mile.

There is an emergency telephone at the beginning of the highway.

How often will an extra telephone be required, if there is to be an emergency telephone between every two consecutive milestones?

(In reply to Probably answer without proof by Larry)

This may not be what is intended, but the problem requires "an emergency telephone between every two consecutive milestones".  If there is a phone "at the beginning of the highway", this is "at" milestone 0, not "between" 0 and 1, so an extra phone is required because both a dist and an ance are >1.

Posted by Kenny M on 2024-07-29 13:28:19