Let's start with an easy one...
An inventor, Bob, uses two robots of the same make to demonstrate their facility in logic. He knows that the robots will execute their demonstration flawlessly.
He tells the two robots to sit on two chairs facing each other with their sides to the audience.
From the audiences perspective, we shall call the robot on the left Robot L, and the robot on the right Robot R.
Bob sticks a postit note on Robot L with some number between 0 and 5 inclusive written on it and tells Robot L that there is a Postit note with a number between 0 and 5 inclusive on its head. Robot L trusts the inventor implicitly, but cannot see what is on its head. Robot R, however, can see what number is posted on Robot L's head.
The inventor then repeats the same procedure with Robot R, except with a number between 0 and 6 inclusive. Robot L, knows what is on Robot R's head, but Robot R does not.
Bob then informs the robots, truthfully, that the 11 minus the sum of the numbers on their heads is either one less or one more than the sum of the numbers on their heads.
The inventor tells the audience that he is going to ask the robots in a roundrobin fashion the following question:
"Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?"
The robot will answer either "yes" or "no."
To Robot L:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot L responds:No
To Robot R:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot R responds:No
To Robot L:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot L responds:No
To Robot R:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot R responds:No
To Robot L:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot L responds:No
To Robot R:Based on the number you see on the other robots head, and the responses so far, can you deduce what number is on your head?
Robot R responds:Yes
What number was posted on Robot R's head, and what was your reasoning for this answer? (c'mon you have a 1 in 7 chance of just guessing right, you need the explanation too)
P.S. Reading comprehension is part of puzzle solving
User Tag List

05092009, 08:33 AM #1
Props to whomever solves my puzzles first
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

05092009, 08:49 AM #2

05092009, 08:59 AM #3
I think it was three. I assume that everytime Robot R was asked the question, the other robot gave a signal indicating the number was higher than the amount of times the question had been asked so far. When Robot R reached the right number, the other robot didn't give this signal, so it knew that three must be the number (because the question had been asked of it three times before).

05092009, 10:46 AM #4
How do I do spoiler tags here?
Robot L's number was 2
Robot R's number was 3
I can show work if you desire.

05092009, 10:51 AM #5
Totally bleached out for pseudospoiler tag majiggerisms.
Robot R's number is 3.
The possible combinations are :
0,5
0,6
1,4
1,5
2,3
2,4
3,2
3,3
4,1
4,2
5,0
5,1
1st Question (directed at L):
0,5
0,6
1,4
1,5
2,3
2,4
3,2
3,3
4,1
4,2
5,0
5,1
Robot L can see R's number, and if R's number was a 6, it would know automatically that it's number was a 0. L answers no however, so both robots now that R's number is not a 6. Same thing with 0.
2nd Question (directed at R):
0,5
1,4
1,5
2,3
2,4
3,2
3,3
4,1
4,2
5,1
L's number cannot be a 0 or 5, or R would know it's number.
etc, etc until the answer is reached.
3rd Question (directed at L):
1,4
1,5
2,3
2,4
3,2
3,3
4,1
4,2
4th Question (directed at R):
1,4
2,3
2,4
3,2
3,3
4,2
5th Question (directed at L):
2,3
2,4
3,2
3,3
6th Question (directed at R):
2,3
3,3
The only possibility is 3. R's number is 3. L's number remains unknown."All humour has a foundation of truth."
 Costrin

05092009, 11:29 AM #6
I'm gonna give props to Costrin.
Athenian got the right answer, but the explanation wasn't quite right.
Rhinosaur extrapolated a little too much, and didn't give the explanation (while Costrin posted just 5 minutes later, and explanation does take a little while to type out).
I'll try to post a little harder puzzle later today. This easy one was just to get things going.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

05092009, 01:10 PM #7
I refuse to answer your question on the grounds that you call such a monstrosity "easy"
...and also on the grounds that I don't know the answer.
The last part is especially illogical to me, as the answer to the exact same question asked seven times is the exact same answer. This is where the trick lies, isn't it?

05092009, 04:49 PM #8
OK, for Luna I'll post an even easier puzzle...a harder one will follow later.

An accused traitor is brought before a chaotic evil Duke. The Duke is very fond of praise especially if it comes from someone he is torturing.
This Duke also uses a magic number for all sorts of things in his castle to give him power. If the number were to fall into enemy hands, he would be in trouble. The Duke is still fairly confident, however, because his magic number could be anything, even something like pi.
The person brought before him is thought to be a spy (and he is).
The spy knows that the Duke is impervious to poisons, as long as he drinks his magic number in mL of poison, twice, before administering it to someone else. Because of this, the Duke always does so.
The spy also knows that the Duke keeps a portion of his poison in a tiny square vial with a width of his magic number in centimeters, with a mark at 1 cm high. The Duke always refills the vial to that mark for some unknown reason. The spy knows this and was after this vial.
The Duke goes into a back room in his castle to perform his usual ritual before poisoning someone.
The spy knows of someone who came back from the castle and died from this ritual poisoning, so his extremely anxious.
But just then he hears the Duke yelling at one of his servants, "You wretch! Where is it?!! Fetch me the magic eyedropper at once! I need to add the ritual mL before drinking my share! No, No! No other magic vial shall do! I am to have less than a mL left after I drink! Do you know how hard that is without that eyedropper?!"
The guard holding the spy down is momentarily distracted by the sound, and the spy uses this opportunity to break free, and run away.
Back at his home, he is visited by the wizard who gave the Duke his magic number and the powers that it bestows. The wizard is very fond of numbers and geometry (hence his use of magic numbers and such).
The wizard tells him, "If you were to measure the volume of the poison after the Duke's ritual drinking, along with the knowledge you now have of his ritual, you would have narrowed down the number of possible values for his magic number. Tell me what number of possibilities that would have been, and I will tell you his magic number."
What should the spy give as the number of possibilities? Once, again, no props without a full explanation.
Also, I am a little off because of my medicine, so if I seemed to have left out a part ask some questions. I may or may not answer them.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

05092009, 06:13 PM #9
I love puzzles! (Ones that don't involve the main character really being a fish or something.)
#1: Heh, they got to it before me!(3!)
#2: My math isn't super, but... this is what I *think*:
If the magic number is N, then the volume of liquid in the vial up to the "line" would be N^2 millileters. Therefore the magician was adding 1 mL to his vial before drinking 2N mL from the vial.
Therefore, I think what the magician was saying was that N^2 (mL) + 1 (mL)  2N (mL)< 1 (mL).
Which simplifies to N(N2) < 0. Which means the magic number N: 0 < N < 2. Assuming I'm reading the problem correctly.

05092009, 06:39 PM #10
^You're on the right track, but you still got to figure out how many possible values there will be.
Also, double check you're math.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
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