## Saturday, November 28, 2009

### White House Party Crashers

A couple from Virginia breezed through the White House security and leisurely enjoyed the State Dinner with the president, vice-president, Indian Prime Minister and an array of other hand-picked guests. All is well, except that the couple has not even been invited to this dinner... Wow!
How did they do it? Rumor has it that the secret service agent asked them "Have you been invited?" They answered: "Yes!" and walked right in. While the Secret Service is trying to figure out how they let it happen, I suggest we help them with some logic. Our world consists of liars and truth tellers. The liars got entangled in their lies so deeply that they always lie, and the truth tellers are always honest. Both, liars and truth tellers, are occasionally being invited to White House parties. And both, liars and truth tellers, may occasionally have an impulse to attempt to crash a White House party uninvited. What question you suggest Secret Service agents ask any party goer, in order to let through only those invited, be it a liar or a truth teller?

(this puzzle is inspired by Giovanni Ciriani's answer to one of our recent puzzles)

To get a correct answer point, please explain your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Anonymous said...

The logic would require both the people to be invited and that they are truth tellers. If they can answer "yes" to this question, they may be admitted.

Maria said...

We can only hope that only truth tellers are being invited to the White House. I am afraid that in real life, and in this puzzle, Secret Service should let anyone invited in. Be it a truth teller or a liar.

Maria said...

I see that quite a few people used our new poll to answer this question. Correct answer, I believe, is #3: Security Service agent should ask:
"Is one of the following true? You have not been invited to this event and you are a liar, or you have been invited and you are a truth teller."

Let us see, how it makes sense:
We have four types of people in this puzzle:
1) liars who are invited to a party
2) liars who are not invited
3) truth tellers who are invited
4) truth teller who are not invited

We know that liars always lie and our task is to let in only those who are invited, be it a liar or a truth teller: option (1) & (3) above. Those, not invited, from option (2) and (4) above, should not be allowed to enter.

When a Secret Service agent asks question #3, how does it fit our types of people?
1) liars who are invited to a party: False
2) liars who are not invited: True
3) truth tellers who are invited: True
4) truth teller who are not invited: False

But note that liar are always telling lies in this puzzle, so their answer will be reversed:
1) liars who are invited to a party: True
2) liars who are not invited: False
3) truth tellers who are invited: True
4) truth teller who are not invited: False

Therefore, anyone answering "True" to the question #3 is indeed invited and should be allowed in. Anyone answering "False" is not invited and should be prevented from entering.

Now, we just need to convince Secret Service to adopt this question :)

New fun puzzle tomorrow.