During my freshman year of university, I enrolled in the Puzzle-based Learning course, which introduced a fresh approach to teaching and learning, emphasizing the enhancement of problem-solving abilities. Throughout the course, I came across numerous intriguing questions that I wanted to share. As a result, I decided to gather these captivating problems and add them to my personal collection before entering my sophomore year.
Question 1 (GPT-4o can answer, but with lengthy calculation. Obviously it cannot find simple answer on the internet)
A man is buying wooden letters. Each letter has a price, but different letters can have different prices. A shopkeeper explains the cost of a few words:
ONE costs $1
TWO costs $2
ELEVEN costs $11
The man wants to buy TWELVE. How much does TWELVE costs?
[Hints: use algebra and no need to calculate the cost of each letter]
Question 2 (GPT-4o can answer with good logical explanation)
Four men named A, B, C and D made statements related to their height:
A: I am the tallest.
B: I am neither the tallest nor the shortest.
C: I am not the shortest.
D: I am the shortest.
Knowing that exactly one of them lied, can you determine who is the shortest and who is the tallest?
[Hint: hypothesis and rule out by contradiction]
Question 3 (GPT-4o gives correct answer but wrong explanation. It does not know how to fine tune the logical thinking by trial and error)
A car carrying an important parcel must cross a desert. There is no petrol station in the desert, and the car's fuel tank is just enough to take it half way across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters or rope to tow the cars. Can the parcel be delivered? If so, what is the minimum number of cars needed and how is the process of delivering the parcel?
[Hint: consider the final requirements and determine the best approach to fulfill them.]Question 4 (GPT-4o can answer with good logical explanation)
There are two communities on an island. One always tells the truth and the other one always lies. A visitor to the island would like some information so she would like to identify a truth teller. She meets two of the locals, let’s call them Alice and Bob. The visitor asks Alice: “Are you a truth teller?” Alice understands the question, but responds on her own language by saying: “tregreg”. Bob notices that visitor’s puzzled look, and clears things up by saying: “Alice says yes, but she is a liar”.
a) Which community is Alice from?
b) Which community is Bob from?
[Hint: use critical thinking]Question 5 (GPT-4o cannot give correct answer. I believe it only finds similar pattern on the internet but do not know how to further manipulate)
1, 2, 2, 4, 5, 9, 13, 22, 34, 56, ...
What are the next three numbers in the above sequence?
[Hints: Each number in a position is influenced by two numbers that come before it]Question 6 (GPT-4o can answer. Obvious it finds the answer on the internet)
3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, ...
What are the next three numbers in the above sequence?
[Hint: Shift the attention away from the numerical values of the numbers.]Question 7 (GPT-4o can answer. Obviously it find similar sentences on the internet)
A man on his deathbed informs his three sons that he will leave them his horses. To the eldest son he leaves half of his horses. To his second son he leaves one third of them, and to his youngest, he leaves one ninth. After he passed away, the three sons went to get their horses, but discovered there were 17 animals. They did not want to sell or kill any of the horses, and they could not think of a way to divide the horses exactly as their father wished. Just then their next door neighbor came riding along on his horse and listened to their problem. Immediately the neighbor thought of a way to divide the horses just as their father had wished. What was his easy solution?
[Hint: Consider the final requirements and determine the best approach to fulfill them.]Question 8 (GPT-4o can answer, but with lengthy calculation. It does not know how to simplify the process)
With a 7-minute hourglass and an 11-minute hourglass, find the simplest way to time the boiling of an egg for 15 minutes.
[Hint: 15 = 11 + 11 -7]Question 9 (GPT-4o can answer, but with lengthy calculation, duplicate and useless information. It does not know how to simplify the process)
The rules of the test are that students are getting 8 points for correct answers and -5 points for wrong answers. There were 26 questions on the test and John’s total score was zero. Assuming that John answered all questions, how many answers were correct?
[Hint: use algebra]Question 10
Nine dots are drawn in a 3 by 3 grid. How do you draw four straight lines through the nine dots, without lifting your pen off the page?
[Hint: think outside the box, disregarding the confines of the nine-dot area]
Question 11
Without using a pen or drawing, can you find the perimeter of the following diagram?
[Hint: moving the lines in your mind] 
End of the quiz
