Something we worked on today in class, I thought I'd share it. THINK THIS THROUGH. There is a solution. I have more to follow.
Three college students are selected to be on the hit TV game show, Dot of Fortune. One of these students has been enlightened to the ways of mathematics, and the other two are sociology majors. on this game show, there are no mirrors, no reflective surfaces, etc. - there is no way to cheat. When the students go on the game show, they are blindfolded and a dot is placed on each one of their foreheads. The blindfolds are removed and they are told that if they see a red dot, they are to raise their hands. In this case, they all have red dots on their heads, so they all raise their hands (they can't see their own dot). Whoever figures out which color dot they have first wins. After a few minutes, one of the students looks up and says "I have a red dot on my forehead." How did he come to this conclusion?
Note: He did not simply guess or speculate, he was absolutely certain he had a red dot. He had not seen his own forehead.
I'm just going to assume that the math guy wins, he person A, the other two are persons B and C.
What would happen if "A" had had a non-red dot on their forehead wile the other two did? Person B or C could have deducted that the only possible way for both others to have their hands raised when only one had a red dot was that they, themselves had a red dot on their forehead and would have answered. Person A therefore waited and when neither B nor C answered realized that he too, must have a red dot.
Ok i think i figured it out. Bare with me. There are two ways of looking at it. Ok the maths person sees a red dot on the forehead the two other players. If the dot on the maths persons head was white the two others would see one red dot and on white dot with two hands raised. Each person would then wonder if they had a red or a white dot.
If they had a the red dotted person wouldnt have a raised hand. Ergo I would have the red dot. After this deduction the person would hit the buzzer.
BUT the other two people didnt hit their buzzers. If the other two had seen a white dot and a red and both had raised their hands they would have also been able to deduce that their own dot was red. Since neither buzzed instantly neither would have seen a white dot on the maths persons forehead. Ergo the maths person waited long enough to realise that they dont know what their own colour was and so finally the maths person buzzed confident their own dot was red.
At least thats what i think is the answer. Am i right?
What would happen if "A" had had a non-red dot on their forehead wile the other two did? Person B or C could have deducted that the only possible way for both others to have their hands raised when only one had a red dot was that they, themselves had a red dot on their forehead and would have answered. Person A therefore waited and when neither B nor C answered realized that he too, must have a red dot.
BUT the other two people didnt hit their buzzers. If the other two had seen a white dot and a red and both had raised their hands they would have also been able to deduce that their own dot was red. Since neither buzzed instantly neither would have seen a white dot on the maths persons forehead. Ergo the maths person waited long enough to realise that they dont know what their own colour was and so finally the maths person buzzed confident their own dot was red.
Both right. Next question!
While on a dig, an archaeologist finds an ancient lamp. Just for laughs, she rubs it. Much to her surprise, a genie comes out and tells her she can have 3 wishes (basic "no wishing for more wishes" rules apply). After pondering this for a moment, she wishes for the Jewel of Medina so that she may become infinitely wealthy and powerful. The genie snaps his fingers and *POOF*! 9 identical stones appear. They all look and feel the same, but the genie states that one is slightly heavier than all the others. However, the archaeologist can only take one stone with her when she goes. Without thinking, the archaeologist says "Gee, I wish I had a balance," and with another snap from the genie a balance appears. It looks like a normal balance, but the genie states that it is a magic balance that will break after one use. "If you want," he says, "You can use your last wish to get another magic balance."
How do you determine with certainty which stone is the Jewel?
YOU MAY NOT WISH YOU KNEW WHICH STONE WAS THE JEWEL. YOU MAY NOT WISH FOR MORE WISHES.
Do you wish that all but the jewel and one other stone are taken away? That isn't wishing to know which one is which, and you can just weigh them. Man, if the answer is math related, there's no way I'll get it.
Ok i think ive got the hang of this. Ive always enjoyed these puzzles Megamickel keep em coming.
Ok this is my second chance to shine.
The archaeologist should arrange the stones into 3 different groups of 3 stones each. Then put one group of stones on 1 side of the scales and the other group on the other side. If the yboth weigh the same then you know the stone is in the third unweighed group. If one is heavier than the other then you know that the stone is in the heavier of the weighed groups. So after this first weigh in the archaeologist knows which group the stone is in.
The archeaologist should take the group which she knows the magic stone is in and put 2 of the stones on one side of the scale and 1 stone on the other side. If one side weighs more than the other then she knows that this side contains the magic stone. But if they both weigh the same then she knows the siide with 1 stone is the magic one.
