While driving to work this morning I was listening to an AM radio station. The station number is a four digit integer. As I preset the station on one of seven buttons on my radio. Then I started thinking about the number ... if was divisible by seven if the second digit is removed. What is the number of the radio station?

Originally posted by petrovitch While driving to work this morning I was listening to an AM radio station. The station number is a four digit integer. As I preset the station on one of seven buttons on my radio. Then I started thinking about the number ... if was divisible by seven if the second digit is removed. What is the number of the radio station?

Not enough information so will have to do some deduction.

1. I see you are in US so I will assume you mean frequency when you refer to station number? (We use wavelength for AM in Europe)

2. I will assume frequency range 535-1705 KHz (US )

3. I will assume 10KHz between stations (in Europe it is 9KHz)

Our number is therefore abcd
where
535 < abcd < 1705
acd = 7n
a=1
b=0,1,2,3,4,5,6,7
c=0,7
d=5

That still leaves 15 solutions, what have I missed?

AM stations generally (always?) end in 0 -- and being that it's a 4-digit number, the first number is a 1

if we eliminate the second digit, you get a three digit number 1e0 -- the only number between 100-199 that ends in 0 and is divisible by 7 is 140, so e = 4

if AM stations max out at 1705, that leaves us with the solutions of 1040, 1140, 1240, 1340, 1440, 1540, 1640

Originally posted by Melanerpes AM stations generally (always?) end in 0 -- and being that it's a 4-digit number, the first number is a 1

if we eliminate the second digit, you get a three digit number 1e0 -- the only number between 100-199 that ends in 0 and is divisible by 7 is 140, so e = 4

if AM stations max out at 1705, that leaves us with the solutions of 1040, 1140, 1240, 1340, 1440, 1540, 1640

Given the range I assumed they ended in 5.

I stand corrected.

The problem with this problem is that you need 'local' knowledge ... and it aslo appears to be cooked!