Curious Coordinates
In the middle of a canal in the quiet town of Kochi lies a small pier with a little monument begging to be seen. Why put a monument in the middle of a canal? Because it's the exact location where the geographical coordinates are 133°33'33"E, 33°33'33"N. There are only eight places in the world with both coordinates containing six consecutive 3s, and this is the only one on land. So numerically, it's a very unique place!
This random fact is celebrated with two bold monuments. One is a metal sphere with wings, standing on a pier in the middle of the canal. The sphere has wings and the number 33 proudly on display. The other monument, on the side of the canal, is a small tower with - you guessed it - 3 legs. And across the street from the tower, there's even a building where you can get a certificate to commemorate this achievement. I rang the doorbell, and a friendly woman welcomed me in. She had me write my name on the certificate, and wrote in the date, signed her name, and even stamped it with an official stamp! It was a very Japanese experience.
There are eight places in the world with six consecutive 3s in both coordinates; however, only the one in Japan is on land:
33°33'33"N, 33°33'33"E - Eastern Mediterranean
33°33'33"S, 33°33'33"E - Near South Africa
33°33'33"N, 33°33'33"W - North Atlantic Ocean
33°33'33"S, 33°33'33"W - South Atlantic Ocean
33°33'33"N, 133°33'33"E - Kochi, Japan
33°33'33"S, 133°33'33"E - Near Southern Australia
33°33'33"N, 133°33'33"W - Near California
33°33'33"S, 133°33'33"W - South Pacific Ocean
Sample Problems
1. How many locations exist on Earth whose coordinates (both latitude and longitude) are all the same digit (like 22°22'22"S, 22°22'22"W)?
2. How many locations exist on Earth whose coordinates (both latitude and longitude) each contain at least six of the same digits?
3. Many of these locations are located on land, but some of them are in places that are rather difficult to get to. Are any of these places located inside of cities, like the one in Kochi, Japan?