Congrats on making it to the advanced page! Be prepared for a challenge that will test your deductive reasoning prowess. You will need a magnifying glass to hunt for clues, a bloodhound's nose to follow the leads and a thinking cap to figure it all out. Watch out for any unnecessary information that might mislead you, and keep your eyes focused on the goal. The hunt is on!
Here are some tips for you to get started:
- Read through the passage carefully and make note of the important information.
- Work from the information that you are given and think about their implications.
- If you're stuck going forward, try working backward!
- Practice, practice, practice!
- Read the solution if you get stumped.
One day a mad scientist lined up Andy, Brandy, Candy and Dandy in a row, so that each of them could see the ones in front of them but not behind. Andy was able to see everyone else while Dandy couldn't see anyone. Then the mad scientist declared,
"There is a red hat, a blue hat, a white hat, and another hat that is either red, blue or white. I will place them on your heads, so that you can't see the color of your own hat. However, you can see the hat color of anyone in front of you."
Starting from the back (Andy first), he asked them each in turn what the color of their hat was. To his surprise, they all were able to correctly deduce the color of their hat based on the responses that they heard.
Which 2 people had the same color hats?
Let's work from the information that we are given, and record down the implications:
- If Andy had seen hats of 3 different colors, then he would not have been able to deduce his own hat color. Thus, he saw 2 hats of the same color and 1 hat of a different color.
- If Bandy had seen 2 hats of different colors, then he would not have been able to determine his own hat color. Thus, he must have seen 2 hats of the same color, and then called out the remaining color.
Thus, Candy and Dandy had hats of the same color. \(_\square\)
Logic puzzles can be classified as
- Logic Word Problems: Working from the given statements, we have to determine if the conclusion is true or false. It can be helpful to rephrase the problem so that it is familiar to you.
- Truth-tellers and Liars: Based on what people said, we have to figure out who told the truth and who lied, in order to determine what happened. Remember: Liars never say “I am a liar!”
- Order Theory: Given how certain terms compare to each other, we have to find the largest or smallest term. Given various comparisons, we have to decide which term is the largest or the smallest. Drawing a flowchart can be helpful, as it offers a visual way for us to get organized.
- Elimination grids: Setting up the information in a grid offers an easy way of displaying an interaction with the information. Cross out scenarios that cannot be true, and "when you have eliminated the impossible, whatever remains, however improbable, must be the truth."
- Information Compression: The information has been compressed, which allows people to communicate extremely effectively, which then can stump an outsider. We have to tease apart the process in order to determine the best way to package the information.
- K-level thinking: When events occur sequentially, we can make use of the information gleamed in the prior step, to restrict the possibilities of the next step. By listing out all possible scenarios, we can easily work through the implications and figure out the true scenario.