Andy says:

Brad is a Liar.

Fred is a Liar.

I'm one year older than Brad.

I'm three years older than Chet.

The sum of our ages is divisible by 3.

Brad says:

Chet is a Liar.

Andy is a Liar.

I'm one year older than Chet.

I'm three years older than Doug.

My age is divisible by 5.

Chet says:

Doug is a Liar.

Brad is a Liar.

I'm one year older than Doug.

I'm three years older than Eddy.

My age is divisible by 2.

Doug says:

Eddy is a Liar.

Chet is a Liar.

I'm one year older than Eddy.

I'm three years older than Fred.

I'm the oldest.

Eddy says:

Fred is a Liar.

Doug is a Liar.

I'm one year older than Fred.

I'm three years older than Andy.

The sum of our ages is divisible by 11.

Fred says:

Andy is a Liar.

Eddy is a Liar.

I'm one year older than Andy.

I'm three years older than Brad.

The sum of our ages is a perfect square.

Figure out the ages of the six natives.