[rsaavedra]

100% can be legitimately saved because of lack of comprehensive constraints in the problem statement

Just for fun, but notice that nothing in the problem statement renders the following strategies invalid:

Strategy 1) All the guys wear a small mirror attached with velcro to the back of their shirts. Hence everyone will be able to guess their color correctly, except for the first guy in the line (last one to guess). Teammate #101 (in the audience) will call just that one guy telling him his hat color the following way: 1 ring == red, 2 rings == green, 3 rings == blue. That guy #1 in the line will have his cell phone in his pocket with mute ringing, just very discrete vibration mode. And just in case, he will have a cell phone that allows you to block any phone call other than those he wants to allow, and during the show he will allow only the number of the guy in the audience, teammate #101.

Strategy 2) Stretching the audience helper strategy a bit, let the 100 guys have their cell phones as in 1, and make teammate #101 call each and everyone of them.

Requirements for success of these lame strategies:
a) Cell phones will work at the show premises.
b) All of them should have charged batteries, and should have their accounts in good standing.
c) For strategy 2, the guy at the audience should be able to identify all of the 100 guys easily during the show and should find the number of any of them in his phonebook and place the call fast enough. Otherwise get sufficient helpers, e.g. 5 of them: teammates 101 to 105, or let's call them A, B, C, D, and E, and assign to each one of them groups of 20 guys to call, spreading the calls required from each as much as possible, as in:
#100 called by A
#99 called by B
#98 called by C
#97 called by D
#96 called by E
#95 called by A
#94 called by B
:
and so and so forth

 

[rsaavedra]

Here's another fun example of taking advantage of insufficient constraints in the problem statement, the famous urban myth of computing building heights with a barometer:

Quote:

The best question has many answers. I am reminded of the story about a student who protested when his answer was marked wrong on a physics test. In answer to the question, "How could you measure the height of a tall building, using a barometer?" he was expected to explain that the barometric pressures at the top and the bottom of the building are different, and by calculating, he could determine the building's height. Instead, he answered, "I would tie the barometer to a string, lower it to the ground and measure the length of the string." His instructor admitted that the answer was technically correct but did not demonstrate a knowledge of physics. The student then rattled off a whole series of answers involving physics — but not one using the principle in question: He would drop the barometer and time its fall. He would make a pendulum and time its frequency at the top and the bottom of the building. He would walk down the stairs marking "barometer units" on the wall. When the instructor finally demanded the "simplest" answer to the question, the student replied, "I would go to the building superintendent and offer him a brand-new barometer if he will tell me the height of the building!" [Collected on the Internet, 1999] The following concerns a question in a physics degree exam at the University of Copenhagen: "Describe how to determine the height of a skyscraper with a barometer." One student replied: "You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building." This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case. The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that showed at least a minimal familiarity with the basic principles of physics. For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use. On being advised to hurry up the student replied as follows: "Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer." "Or if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper." "But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in the gravitational restoring force T =2 pi sqr root (l /g)." "Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up." "If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building." "But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'." The student was Niels Bohr, the only Dane to win the Nobel Prize for physics.

 

[toor]

After I posted my solution I realized you could save 99. At first I thought there were 4 total possible parity combinations, and that u needed 2 bits to describe them. However when I thought about it some more i realized that you could use 1 digit for the error checking. But was too lazy to work/right it out. But yeah 99 saved beats me

.

 

[The_Mac]

Quote:

Originally Posted by TWIFOSP Except that solution assumes an equal distribution of hat color types among the contestants, which was not stated in the problem. It was also not stated that the doling out of the hats is done at random. Since these conditions were never stated, really the only factor is the law of independant trials. Which would state a given hat in front or in back of you has no bearing on what hat was randomly selected for you. All things considered, all hats could be green. So mathmatically, there really is no strategy that can be devised, and the probabily of correct guesses is roughly 1/3rd. So I'm not sure if this is a trick question, or merely relevant information neccesary to correctly solve the problem was left out. Never assume!

Dude, it's a simple expansion of a binary error-checking scheme to a trinary system. That error checking method is actually great for any sequence of "digits" and scales to as many different values as you like, while still needing only one "digit" to store the parity. You could have a million colours and as long as everyone knew what the value of each colour were, you would still need only one "digit" to store the parity. It's a simple checksum.

Believe me, it works, ask any computer-scientist (not programmer) and they'll explain it to you if they have time, let you provide any examples you like, randomly assign the colours, and do all the math yourself, and you'll still get the right answers. It works.