Puzzles to puzzle you - Page 3

Ashutosh · 03-12-2010, 01:16 AM

Geometric puzzles:

(1) Suppose that every point in plane is coloured red, blue or green. Show that there are two point of same colour which are at a unit distance from each other.

(2) Suppose that every point in plane is coloured red or blue. Show that there is a colour such that there are points of this colour at all possible distances.

(3) Show that you cannot cover the plane by any collection of pairwise non-intersecting circles (i.e., boundaries of circles) of positive radii.

(4) Show that the space can be covered with such circles.

abhisays · 04-12-2010, 07:16 AM

Quote:

Originally Posted by Ashutosh

Here's another puzzle:

A person X chooses a number between 1 and 16 - so he has 16 choices. You have to guess the number he chose. You can ask him 7 yes/no questions.

Such a question may be:

"Is your number bigger than or equal to 9?"

X is an honest person and won't lie more than once. He may be too honest and could even answer all 7 questions correctly. You don't know beforehand. At the end of these 7 questions, you have to tell X what number he chose.

So the question is: Find a strategy to do this.

If this seemed too easy, show that 6 questions aren't enough to do the job.

Let me try this puzzle.

Think of the number in base 2, it has a form abcd where each one of a, b, c, d is either 0 or 1. Now in the first 3 questions I will ask him if a, b, c are 0 whereas in the fourth question I would ask him if he lied in one of the last three questions if he says no then you have 3 more questions to figure out the last digit.

He might have lied in one of these questions but I can repeat my question and see if he lied the difficult case is when he says that he did lie in one of the first three questions then I know that one of the digits a, b, c is wrong so in the next two questions I would ask if a is wrong and if b is wrong so 4 + 2 questions and you know a and b and c correctly you can ask d in the last question. Now this should work because he has already used up his one lie so he must give the right value of d in the last question

jitendragarg · 05-12-2010, 05:48 AM

@abhisays

should work, although I am still trying to think how to figure out the fourth digit, if he lies on the fourth question, i.e. when you ask him if he lied in first three questions or not. Say, he didn't lied in any of the three questions, and lies in fourth one, and tells you that he has lied earlier. Now, in that case, what will be your fifth question?

03-12-2010, 01:16 AM	#21
Ashutosh Member Join Date: Feb 2010 Location: Madison Posts: 12 Rep Power: 0	Re: Puzzles to puzzle you Geometric puzzles: (1) Suppose that every point in plane is coloured red, blue or green. Show that there are two point of same colour which are at a unit distance from each other. (2) Suppose that every point in plane is coloured red or blue. Show that there is a colour such that there are points of this colour at all possible distances. (3) Show that you cannot cover the plane by any collection of pairwise non-intersecting circles (i.e., boundaries of circles) of positive radii. (4) Show that the space can be covered with such circles.

05-12-2010, 05:48 AM	#23
jitendragarg Tech. Support Join Date: Dec 2009 Location: Bangalore Posts: 2,771 Rep Power: 35	Re: Puzzles to puzzle you @abhisays should work, although I am still trying to think how to figure out the fourth digit, if he lies on the fourth question, i.e. when you ask him if he lied in first three questions or not. Say, he didn't lied in any of the three questions, and lies in fourth one, and tells you that he has lied earlier. Now, in that case, what will be your fifth question? __________________