Awareness Tests
How well can your brain focus and what happens when it does that? Watch these two awareness tests and you may get surprised by the results.
Students with Hats
Professor Vivek decided to test three of his students, Frank, Gary and Henry. The teacher took three hats, wrote on each hat a positive integer, and put the hats on the heads of the students. Each student could see the numbers written on the hats of the other two students but not the number written on his own hat.
The teacher said that one of the numbers is sum of the other two and started asking the students:
— Frank, do you know the number on your hat?
— No, I don’t.
— Gary, do you know the number on your hat?
— No, I don’t.
— Henry, do you know the number on your hat?
— Yes, my number is 5.
What were the numbers which the teacher wrote on the hats?
SOLUTION
The numbers are 2, 3, and 5. First, we check that these numbers work.
Indeed, Frank would not be able to figure out whether his number is 2 or 8. Then, Gary would not be able to figure out whether his number is 3 or 7, since with numbers 2, 7, 5, Frank still would not have been able to figure his number out. Finally, Henry can conclude that his number is 5, because if it was 1, then Gary would have been able to conclude that his number is 3, due to Frank’s inability to figure his number out.
Next, we we check that there are no other solutions. We note that if the numbers are 1, 4, 3, or 3, 2, 1, or 4, 1, 3, neither Frank nor Gary would have been able to figure their number out. Therefore, if the numbers were 1, 4, 5, or 3, 2, 5, or 4, 1, 5, Henry would not have been able to figure his number out. Thus, 5 is not the largest number.
Similarly, if the numbers are X, X + 5, X + 10, or X + 5, X, X + 10, once again, neither Frank nor Gary would have been able to figure their number out. Therefore, if the numbers were X, X + 5, 5, or X + 5, X, 5, Henry would not have been able to figure his number out.
The Pizza and the Clock
How can you split a pizza into 11 equal pieces, using just one clock?
SOLUTION
The hour and minute hands of a clock overlap exactly 11 times throughout the day. Keeping the clock in the center of the pizza, just make the cuts along the lines defined by the hands during these times.
Parable of the Polygons
Boat on the River
Two men come to a river. There is no bridge, the water is freezing cold and there is only one single-seated boat on the shore. However, both people succeed to cross the river. How is this possible?
SOLUTION
The two men approach the river from the opposite shores.
The Temple Bar
Get from START to FINISH in this landscape maze, created by Matthew Haussler.
SOLUTION
The solution is shown below.
Resting Tire
Which tire does not move when the car turns right?
SOLUTION
The answer is THE SPARE TIRE.
Throw It and Bring It Back
If you throw me from the window,
I will leave a grieving wife.
Bring me back but in the door,
And you’ll see someone giving life.
What am I?
SOLUTION
The answer is THE LETTER N.
The Ping Pong Puzzle
Three friends – A, B, and C, are playing ping pong. They play the usual way – two play at a time, the winner stays on the table, the loser lets the third one play. If you know that A played 10 matches in total, B played 15 matches in total, and C played 17 matches in total, who lost the second game?
SOLUTION
A lost it. Since there have been (10 + 15 + 17) / 2 = 21 games played in total, and each player never misses 2 games in a row, the only way for A to play just 10 games is if he plays the 2nd, 4th, 6th, etc. games, and every time loses.
The Troll Brothers
There are four troll brothers – Wudhor, Xhaqan, Yijlob, and Zrowag.
- Wudhor always says the truth.
- Xhaqan always lies.
- Yijlob lies or says the truth unpredictably.
- Zrowag is deaf and never answers.
You must ask these brothers four YES/NO questions (one troll per question), and figure out their names. What questions would you ask?
SOLUTION
Coming soon.
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