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Best Puzzles

This is collection of the best puzzles selected for year 2012 out of +10K brain teasers. Link to solution is under each puzzle. The answer is usually in spoiler which you can unhide by clicking the "Show" button. Some of them might be quite hard, however, you don't need any deep math knowledge. Just basic logic, creativity and patience is needed.
Here they come - BrainDen Top 10 Puzzles.
Enjoy!

1. Weighing in a Harder Way

You've got 27 coins, each of them is 10g, except for 1. The 1 different coin is 9g or 11g (heavier, or lighter by 1g). You should use balance scale that compares what's in the two pans. You can get the answer by just comparing groups of coins.
What is the minimum number weighings that can always guarantee to determine the different coin.

2. Hats On A Death Row

You are one of 20 prisoners on death row with the execution date set for tomorrow. Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:
"I'm gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....).

The prisoner in the back will be able to see the 19 prisoners in front of him. The one in front of him will be able to see 18...

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer "BLACK" or "RED". If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on...

Well, good luck tomorrow, HA HA HA HA HA HA!"

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many?

 

3. The Liar, The Truth Teller and The Random Answerer

Yes No Maybe Cube

There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no question to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total.
What are your questions and to whom will you ask them?

4. Truth in Packaging

Three boxes are all labeled incorrectly, and you must get the labels right.
The labels on the boxes read as follows:

Box 1
nails
Box 2
screws
Box 3
nails and screws

To gain the information you need to move the labels to the correct boxes, you may remove a single item from one of the boxes. You may not look into the boxes, nor pick them up and shake them, etc.

Can this be done? If so, how? If not, why not?

5. One Girl - One Boy

Teanchi and Beanchi are a married couple (dont ask me who he is and who she is)! They have two kids, one of them is a girl. Assume safely that the probability of each gender is 1/2.
What is the probability that the other kid is also a girl?
Hint: It is not 1/2 as you would first think.

6. Whatchya Gonna Do (2 Goats and a Car)

You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats. If you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open. What should you do?
Hint: It is not 1/2 as you would first think.

7. Sequence Puzzle

The below is a number puzzle. It should be read left to right, top to bottom.
Question 1: What is the next two rows of numbers?
Question 2: How was this reached?

       1
      1 1
      2 1
    1 2 1 1
  1 1 1 2 2 1
  ? ? ? ? ? ?
? ? ? ? ? ? ? ?
              

8. How Did It Happen?

How

A man runs a mile south, a mile west, and a mile north and ends up back where he started! How did it happen?
That might be easy but the harder part is that there are actually an infinite number of answers for where the man could have started from. Explain.

9. Hole in a Sphere

A 6-inch hole is drilled through a sphere. What is the volume of the remaining portion of the sphere?
Clarifications:
[1] the hole is a circular cylinder of empty space whose axis passes through the center of the sphere - just as a drill would make if you aimed the center of the drill at the center of the sphere and made sure you drilled all the way through.
[2] the length of the hole [6 inches] is the height of the cylinder that forms the inside surface once the hole is drilled. picture the inside surface as viewed from inside the hole and measure the length of that surface in the direction of the axis of the drill.
in this sense, you could for example drill a 6-inch hole through the earth. the diameter of the hole would be huge, and you'd just have a tiny remnant of the earth left. but if you could set it on a table [a big table] it would be 6 inches high.
You of course could not drill a 6-inch hole through a sphere whose diameter was less than 6 inches. This fact leads to the logical answer.
The hard way involves calculus. The easy way uses logic.

10. Help! A Remainder is Chasing Me

I just found a number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.

Find the smallest number with such property.

Bonus! Riddle Encore

Apple Pie

Sir, I bear a rhyme excelling
In mystic force and magic spelling
Celestial sprites elucidate
All my own striving can't relate




Oldies but Goodies:

Old Funny One

Right now Mum is 21 years older then her child. In 6 years her child will be 5 times younger than she.
Where is Daddy?

Trapped

There is a room with no windows, doors, or any sort of opening, the walls are solid steel 10 feet thick, and you are trapped inside, left only with a saw and a table.
How do you escape? (more variations in our Brain Teasers Forums)

How Many Were Going To Saint Ives?

As I was going to Saint Ives,
I crossed the path of seven wives.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kittens,
Kittens, cats, sacks, wives,
How many were going to Saint Ives?

Another Oldie - Can You Get Them All?


  1. 26 L of the A
  2. 7 D of the W
  3. 7 W of the W
  4. 12 S of the Z
  5. 66 B of the B
  6. 52 C in a P (W J)
  7. 13 S in the U S F
  8. 18 H on a G C
  9. 39 B of the O T
  10. 5 T on a F
  11. 90 D in a R A
  12. 3 B M (S H T R)
  13. 32 is the T in D F at which W F
  14. 15 P in a R T
  15. 3 W on a T
  16. 100 C in a D
  17. 11 P in a F (S) T
  18. 12 M in a Y
  19. 13 is U F S
  20. 8 T on an O
  21. 29 D in F in a L Y
  22. 27 B in the N T
  23. 365 D in a Y
  24. 13 L in a B D
  25. 52 W in a Y
  26. 9 L of a C
  27. 60 M in an H
  28. 23 P of C in the H B
  29. 64 S on a C B
  30. 9 P in S A
  31. 6 B to an O in C
  32. 1000 Y in a M
  33. 15 M on a D M C
 

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