Ball Thrower
How can you throw a ball and have it come back to you, even though the ball is not attached to anything, doesn’t bounce off anything and nobody catches it and throws it back to you?
SOLUTION
Throw it straight up in the air.
Category: Brain Teasers
A collection of Math, Chess, Detective, Lateral, Insight, Science, Practical, and Deduction puzzles, carefully curated by Puzzle Prime.
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Gold and Nickel
You have 15 identical coins – 2 of them made of pure gold and the other 13 made of nickel (covered with thin gold layer to mislead you). You also have a gold detector, with which you can detect if in any group of coins, there is at least one gold coin or not. How can you find the pure gold coins with only 7 uses of the detector?
SOLUTION
First, we note that if we have 1 gold ball only, then we need:
- 1 measurement in a group of 2 balls
- 2 measurements in a group of 4 balls
- 3 measurements in a group of 8 balls
Start by measuring 1, 2, 3, 4, 5.
- If there are gold balls in the group, then measure 6, 7, 8, 9, 10, 11.
- If there are gold balls in the group, then measure 5, 6, 7.
- If there are no gold balls among them, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 8, 9, 10, 11, so we can find the gold balls with the remaining 2 measurements.
- If there are gold balls in 5, 6, 7, then measure 5, 8, 9. If there are gold balls there, then 5 must be gold, and we can find the other gold ball among 6, 7, 8, 9, 10, 11 with the remaining 3 measurements. If there is no gold ball among 5, 8, 9, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 6, 7, so again we can find them with only 3 measurements.
- If there are no gold balls in the group, then measure 5, 12, 13.
- If there are no gold balls among them, then measure 14, 15. If none of them is gold, then measure individually 1, 2, and 3 to find which are the 2 gold balls among 1, 2, 3, 4. Otherwise, there is a gold ball among 1, 2, 3, 4, and among 14, 15, and we can find them with the remaining 3 measurements.
- If there are gold balls among 5, 12, 13, then measure 5, 14, 15. If none of them is gold, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 12, 13, so we can find them with 3 measurements. Otherwise, 5 is gold, and again we can find the other gold ball among 1, 2, 3, 4, 12, 13, 14, 15 with 3 measurements.
- If there are gold balls in the group, then measure 5, 6, 7.
- If there are no gold balls among 1, 2, 3, 4, 5, then we measure 6, 7, 8.
- If there are gold balls in the group, then measure 9, 10, 11, 12, 13.
- If there are no gold balls among them, we measure individually 6, 7, 8, 14.
- If there is a gold ball among 9, 10, 11, 12, 13, then there is another one among 6, 7, 8. We measure 8, 9. If none of them is gold, then we can find the gold among 6, 7, and the gold among 10, 11, 12, 13, with 3 measurements total. If there is a gold ball among 8, 9, then we measure 10, 11, 12, 13. If none of them is gold, then 9 is gold and we find the other gold ball among 6, 7, 8 with 2 more measurements. If there is a gold ball among 10, 11, 12, 13, then we can find it with 2 measurements. The other gold ball must be 8.
- If there are no gold balls in the group, then measure 9, 10.
- If there are no gold balls among them, then measure individually 11, 12, 13, 14.
- If there are gold balls among 9, 10, then measure 11, 12, 13, 14. If there is a gold ball among them, then there is another one among 9, 10, and we can find them both with 3 measurements. Otherwise, we measure 9 and 10 individually.
- If there are gold balls in the group, then measure 9, 10, 11, 12, 13.
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.
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.
Resting Tire
Which tire does not move when the car turns right?
SOLUTION
The answer is THE SPARE TIRE.
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.
Source:
Strips in the Plane
Prove that you can not cover the plane with infinite strips which have
SOLUTION
Take a circle with radius 1 in the plane. A strip with width X covers at most an area of 2X of the circle. Therefore all strips cover at most an area of 2, which is smaller than the total area of the circle (~3.14).
Shuffling Cards
52 cards – 2 of clubs to Ace of clubs, 2 of diamonds to Ace of diamonds, 2 of hearts to Ace of hearts, and 2 of spades to Ace of spades – are arranged in a deck. We shuffle them in the following manner:
- We take the top card and put in a random place inside the deck.
- Once we get to the King of spades and put it somewhere in the deck, we stop.
Show that this method shuffles the deck uniformly, i.e. every permutation has the same chance to appear.
SOLUTION
Notice that at all times the cards below the King of spades are shuffled uniformly. Therefore at the end, after we put the King of spades in a random place inside the deck, the entire shuffle will be uniform as well.
