No  one solved the riddle from two weeks ago (hats), i'm still wating for the answer.

Light bulbs

You are standing in front of a wall with 100 light bulbs and 100 switches numbered 1 to 100.
the light bulbs  are all off, and the switches have the following effect:
flipping a switch will change the state of all the bulbs that are multiples of that switch (so flipping 10 will change the state of 10,20,30,40..100)
you decide to flip the switches one by one, how many light bulbs will be lit at the end?

flipping the first switch(1) will turn all the bulbs on, flipping the second (2) will then turn off all the even numbers etc... finally turning the 100th switch (100) will change the state of the 100th bulb.


enjoy.

In a really harsh prison the sadistic warden decided to give 100 prisoners the following task:
They must stand in a line, and he will put a hat on each of their heads. The hats can be either black or white. Then each prisoner will be allowed to say one word, either "black" or "white", trying to guess what hat he has. At the end of the game, all prisoners who got their color right will be released, all the rest will be killed. If any prisoner brakes any rule (looks backwards, says any other word, jumps , pokes, etc..) everyone will be killed.

What is their best strategy to get the minimum amount of prisoners killed ? How many prisoners are risking their lives using such a strategy?
The can decide on the stratagy ahead of time.

Again the rules. They all follow the algorithm. They can all hear what the fellow prisoners say. Each prisoner can see all the guys ahead of him , but non of those behind. They can all say either "black" or "white" once but the order of talking is
whatever they want. The number of black and white hats is unknown (but there are  100 hats in total). 

Hi all,
The only person to send me an answer to last week's riddle was Johann. So this week I'm going for an easy one with the promise of a really hard one next week.

After building a 100 story tower, the engineers were faced with a new problem. What's the highest level from which you safely throw an egg without it braking. As usual with the budgeting of such large projects, getting money for the little things is hard and the engineers were given only two eggs to find the maximum height. This could be an easy problem , but being computer engineers rather then civil engineers they decided they must find the fastest "worst case" method of getting the answer i.e the minimum number of eggs throws in the worst case scenario.

here is an example of a bad method. start on the first floor and throw the egg, if it doesn't break go to the second etc.. until the egg breaks. In the worst case this will require 99 tests.

Remember you have 2 eggs, and by the end of the test , both can (and should) be broken.

What is the minimum number of throws in the worst case? (what algorithm do you use).

You can send the answer by email.

Hint: the number is between 2 and 34.

At Johann's suggestion I will try to post a riddle on the blog each week. The first person to get it right will win a chance to buy me a cup of coffee (double macchiato please), so will anyone else who gets the answer etc...

If I come across some quantum riddles I will post them as well but the ones I have at the moment are all classical.

The next one has already been solved by a few people.

The king decided to test his adviser's abilities by giving him the following task:

The advisor will be put in a room with a round table in the middle. At the center of the table is a lamp and at the 4 corners are [0,1] switches. (how do round tables have 4 corners? the switches are on the circumference at 0,90,180 and 270).

The lamp will only work if all switches are at the same position (all 0 or all 1). But it is impossible to tell if a switch is in a 0 or 1 position (like the switch on a cell phone). There is another catch. The main power supply to the room is located in another building and when the power is on the table starts spinning in an unpredictable random manner (using a quantum random number generator).

The king wants to know what the minimal number of steps the advisor has to take in order to be sure the light is on. A step is counted every time the main power supply is turned on. To avoid any confusion, the only moves you're allowed to make are:

1. flipping a few switches,

2. going out and turning the main power supply

3. going back to see if the light is on

4. switching the power supply back off and back to 1.

After a long flight which included going past 2 very unfriendly American airports (LAX and Minneapolis), I finally arrived in Waterloo. Very soon i discovered something very nice about the university there, things are actually open till late, in fact the student center is open 24hrs - wow! and it's possible to get dinner at night. Promising? yes, but it turns out Waterloo is pretty boring after all. The next day i went to the Niagara falls which turned out to be a great way to get rid of jet lag. The falls are pretty impressive, but even more impressive is the amount of tourists there. And all taking photos of themselves.

                         

The conference ended on Sunday with a day of discussion about the future of quantum foundations. It's really great to be a part of this project.



After taking some papers from people and some advice on how to continue with my research (and life in general) I took the bus to Toronto.

Toronto... what a great city, people in the streets, bars, restaurants , homeless bums.... Our first dinner was at a microbrewery :). Monday morning we went to the first day of school at the fields institute,


                         

most of the students were Canadian , but with the 4 of us and one of the lecturers (Vidal) from UQ , Australia was well represented.The students were from all different fields (physics, mathematics, and computer science) and the school was at the level where we could (read should) all understand the different lectures. While not too much was new to me , it was really great to have everything connected in a nice way and to get a good overview of the subject. Oh yeah...  there was a huge blackboard with chalk and everything there.

  On one of the evenings Lauri and I went to a baseball game, it was quite a cultural experience and a very boring game.

Finally we attended the student conference on Saturday and Sunday. The lectures were all very good and again helped me get a good overview of what people are doing (in Canada). I gave my presentation on Saturday and even won a prize, wooohoo. On Saturday we also got to see one of Johann's favorite bands in concert , great stuff. Sunday continued with even better talks then Saturday, and it was a good thing it was the end of the academic part of the trip because i was a little past my saturation point.

                                 

On Sunday night Lauri and I left for New York, after some really rude people at the U.S border crossing we finally got there. Our three days of walking around the city by day and Jazz by night were absolutely fantastic and would have been an amazing ending to our trip had the plane from NY to LA left on time. Unfortunately it got delayed by about 3 hours because the sink in the toilet was not working, for us that meant a whole day in LA. We got to see Santa Monica beach and eat some  real Mexican food . 

All in all , a great trip, both for the mind and the soul.

An audio stream of my talk + the presentation can be found at:
http://www.fields.utoronto.ca/audio/09-10/student_conf/brodutch/index.html?36;large#slideloc