Consider the integer powers of 7: a(n) = 7^n:
7, 49, 343, 2401, 16807,... 117649, ...
Prove that the second from right digit in all those numbers (excluding the 1st) is either 0 or 4.
On a train, Smithe, Robins, and John are the fireman, conductor, and the engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smithe, a Mr. Robins, and a Mr. John.
Mr. Robins Lives in New York.
The conductor lives exactly halfway between Columbus and New York.
Mr. John earns exactly $20,000 per year.
The conductor's nearest neighbor, one of the passengers, earns exactly three times as much as the conductor.
Smithe beats the fireman in billiards. The passenger whose name is the same as the conductor's lives in Columbus.
Who is the Engineer?