How come the bulb is on without any electricity?

One more time (this time with a very different job) I find myself on a Thursday evening flying from DC to Atlanta. Which means time for another puzzle.

This time it is one of those about measuring arbitrary time with those dratted hourglasses. If you are reading this on FB, you probably remember that you can ask clarifying questions in the comments section but send answers by messaging me.

You have two hourglasses – one empties in four minutes and the other empties in seven minutes. You have to bake a cake but it must be baked for exactly nine minutes. What is the minimum time it will take you after I say Go! for you to bake the cake? (You don’t have to start baking the cake immediately when you turn the hourglass(es) but once you start baking, it has to finish in exactly nine minutes).

To further clarify, if you said “I will flip the four minute hourglass first and then moment it is done, I will start baking and flip both hourglasses….. And say you figured out how to bake the cake in nine minutes now using those two hourglasses”, then total time taken is thirteen minutes. Get it?

Go!

What is a common trait to Nokia, Microsoft, Pepsico, Citibank and Adobe?

On a coast to coast flight. Figured I have enough time to come up with a puzzle.

As always send a personal message for your answer – do not put it in a public place like Comments section in Facebook.

I had heard this problem long time back and was struck by the simplicity of its answer. I am adding a twist to that question here.

You and fourteen more of your team members were having coffee at your office cafetaria one day. Your manager walked up to you and said “I have an interesting problem for you guys. All of you will get an increment if you can tell me the correct answer. I am going to pick a random person ten minutes from now and ask – ‘how many of the team members earn higher than the average salary of the team’ ?”

Now the trick is obviously nobody wants to divulge their own salary to anybody else. And nobody wants anybody to know whether he or she is making higher or lower than the average.

You can assume nobody is earning at exactly the average number.

The team members look up to you to devise a quick, easy and elegant way so that everybody will get that increment.

How would you do it?

This is one of those “shunting” puzzles. As you can see in my somewhat clumsy diagram, there is a railway track that goes indefinitely to the right. On the left, it splits into a “Y”, both ends of which merge into a finite straight railway track. There is a coach “A” sitting on one arm of the Y and another coach “B” sitting on the other arm. Both the coaches are 5 yards each.

The distance between the junction point on coach A side and the end of the finite straight track is 5 yards. On the other side, near coach B, the distance between the junction point and the end of the straight finite track is 15 yards. (See pic). In between the junction points on the straight track sits an engine “E” which is itself 10 yards in length.

Like every engine, E can go forwards or backwards and can pull or push the coaches. Any coach and engine can be attached to each other.

Here is the puzzle: Can you interchange the position of coach A and coach B? You have to get engine E back to its original position when you are done.

Two students of maths are playing the following game – each takes turn to pick a number from the following set {-4, -3, -2, -1, 0, +1, +2, +3, +4}. Once a number is picked, it is not replaced. And they keep playing till they run out of numbers. And they start all over again.

Whoever can come up with three numbers that add up to 0 first wins the game. It does not have to be the only three numbers she has. For example, she might have picked -3 and then in next chance picked +2. Hoping to pick +1 next. But other player seeing that, would  have taken away the +1 in the next move. So let’s say the original person next picked 4. And then if she got a chance to pick -1 in the next move, she would have -3, +2, +4 and -1. Note that -3, +4 and -1 adds to 0. So she wins.

Now, here is the question: If you are the first player, is there a strategy for you to win? If you are the second player, is there a strategy for you to win?

If you are seeing this in FB, send me message and do not post answers in Comments section.

This puzzle does not require math skills but some imagination and visual skills. Assuming you have not seen this problem before, that is. One of the visual skills required is getting past my terrible drawing abilities 🙂
So, there is a painting with a string attached on the top two ends as shown in the picture. And there are two nails on the wall horizontally separated. (the separation distance does not matter).
Can you hang the painting with the string in a way that if any one of the nails come off, the painting will fall down to the ground?
Of course, the painting needs to actually hang from the nails using the string.

Thursday evening. No flight today. I got done with it on Monday. But still there is a puzzle…

Thursday morning flight back home from Maryland and New Jersey. Puzzle time!!!

Since last week I was pilloried for lowering my standards of puzzle (once again, I am amazed that people think I have standards), I picked a slightly harder one this week. I heard a variation of this in Car Talk last week as I was taking Tasha somewhere.

If you know this, you will get it immediately. If you had heard this before, it is fun trying to remember the answer. If you have never heard it before, it would be interesting to solve it. Let me know thru FB message if you would like some hints.

As always, do not write on comments section if you have figured it out. This is to give others a chance to solve it. Send me a FB message.

There is a slightly easier version and a slightly tougher version of this puzzle. The puzzle goes roughly like this.

There is a prison with 15 prisoners for life in individual cells with no ability to communicate with each other whatsoever. One day, the warden took all of them out and gave them a chance to go out free. However, there was a catch.

He showed them an isolated room from outside in a separate part of the jail and told them that there were two switches inside. One on the left and the other on the right. The switches were connected to absolutely nothing. They could only be flipped to the on or off position.

The warden, starting the next day, was randomly going to pick a prisoner – at random times (could be few a day or could be none some day) – and take him inside the room. While inside, the prisoner would have to flip any one switch once. (If it is on, he flips it off and vice versa). However, he had to flip one (and only one) switch. He could choose which one to flip, of course.

Slightly easier version: The warden told them that both the switches were initially in off position.

Slightly more difficult version: The warden told them that nobody – including himself – knew what the starting positions of the switches were.

And then the warden said – “I need somebody among you – I don’t care who – some day – I don’t care when – to come and tell me that you are confident that all the prisoners have visited the room at least once. If that person is right, all of you go scott free. If not, all of you will be put to death.”

He gave them sometime to get together that day to devise a strategy to see if they could come up with a foolproof plan to get out.

Can you suggest a strategy (for both the easier and more difficult case)?

Remember, they don’t need to tell immediately after all of them have visited once. They just need to be absolutely sure that each one of them has visited the room at least once.