Of all the puzzles I have come across, two stand out. These puzzles stand out in my mind, because of their complexity and the mental gymnastics demanded to solve them. First, the one about the fox, the chicken and the corn.
The other, is about an island with two tribes, one tribe always lies, the other always tells the truth.
You are on an island. On this island there are two tribes. One tribe always tells the truth. The other tribe, always lies. You come to a fork in the road and meet a native. You don’t know if he is from the tribe that always tells the truth or if he is from the tribe that always lies. One of the roads leads to a safe destination, the other leads to your death.
Clue: You can ask only one question of this native, and the answer will take you to the safe place no matter what tribe the native is from.
If you want to attempt to figure out this puzzle don’t read below the diagram. To see how I used numbers to figured it out – keep going.
How can this puzzle relate to numbers? After some thinking, I found it. This puzzle was about truth and lies. Truth is positive and Lies are negative. Thats it!
The truth will be represented by positive numbers, for example, 1 or (+1). The lies will be represented by negative numbers, for example -1. In order to get to the safe spot I will need get an answer that is “positive”. A “negative” answer will take me to the wrong place.
The truth teller will point to the right direction. His answer will be always be positive. The person we need to be concerned about is the one that tells lies. That is where the answer will be.
So how do you change a negative into a positive? The only way a negative number can become a positive number is by multiplying it by another negative number.
At this point, I knew I was on the right path and I abandoned the puzzle. I let it sit for a couple days and on the 3rd day, it came to me. It’s a technique for solving puzzles. I analyze the info, come to a temporary conclusion and then I put it away. By filing it into the “temp” folder, it activates a behind the scenes, subconscious exploration.
I had to figure out a way to turn a “positive” question into a “negative” question. After a lot of pondering, I found that by adding the word “if” in front of a question, I could remove the value of the question and make it act, as if it was a “non-question” or a “negative” question.
Here is the question.
“If I was to ask you, what was the way to the safe spot, what would you have told me?
By making the question a hypothetical and by placing it in the past we are able to make the pathological liar, lie about what he would have said, and in effect tell us the truth. It’s like a negative multiplied by a negative.
This question will make either tribe point to the safe place.