At a family reunion, I met four distant cousing who are all in the US military. They each came in their dress uniforms, two from the Army, and two from the Navy. When I asked them their names, and where they were stationed, Terry and Tracy told the truth, but Lee and Loren lied. This was especially confusing because all four names could belong to either a man or a woman. Here is what they each said:

Male soldier:

1. The male sailor is Terry.
2. Tracy isn't stationed in Afghanistan.

Female soldier:

1. The female sailor isn't Terry.
2. Loren isn't the person stationed in Texas.

Male sailor:

1. The male soldier is Lee.
2. The female sailor is Loren.

Female sailor:

1. A sailor is stationed in Hawaii.
2. Tracy is stationed in Afghanistan.

Help me figure out who is who, and where they are all stationed (one is in Kuwait).

(In reply to Answer by K Sengupta)

At the outset, we observe that the male soldier’s (ms) second statement directly contradicts female sailor’s (fl) second statement. Also, the male soldier’s first statement directly contradicts female soldier’s (fs) first statement.

Thus, the possibilities are:
(ms, fl, fs) = (t, l, l), or: (l, t, t). If  the former choice is true, then by ms’s first statement it follows that the male sailor (ml) is Terry, so that Tracy is the male soldier. Then the first statement of ml (Terry) is false. Thus, (ms, fl, fs) =  (l, t, t).

Thus both the female combatants are speaking the truth. Since by fs’s first statement, the female sailor (fl) isn't Terry, she must be Tracy. Hence, Terry must be the fs.  By fl’s second statement, it follows that Tracy is stationed in Afghanistan.

Since both the male combatants are liars, their names are: Lee and Loren. By ms’s first falsely stated statement it follows that the ms is Loren, so that: ml must be Lee.

Now, by fs’s second statement, Loren is not stationed in Texas. He cannot be stationed in Afghanistan, as Tracy is already stationed there. So, Loren must be stationed either in Hawaii, or Kuwait. By fl’s first statement, a sailor is stationed in Hawaii. Since Loren is not a sailor, and since the fl (Tracy) is already stationed in Afghanistan, it follows that the ml(Lee) must be stationed in Hawaii, and accordingly Loren must be stationed in Kuwait. The remaining station, that is Texas must then be assumed by the fs (Terry).

Posted by K Sengupta on 2009-02-01 13:51:52