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.
The archaeologist measures three stones against another three. She either takes the heaviest set of three or if they are of equal weight the three left out. She then wishes for a second balance and weighs one of those three against another one of the three. She either takes the heavier one, if both are of equal weight she takes the stone that was set aside. Then she leaves as the wealthiest, most powerful person ever.
Alternate: The archaeologist realizes money and power aren't everything and uses the final wish for a happy life, world peace, food for the hungry, etc. Then she takes one of the jewels at random to sell.
Alternate: The genie said one of the jewels is heavier but never said that was necessarily the Jewel of Medina. The archaeologist takes the heavier jewel but doesn't have infinite wealth/power.
I can't think of how you could do this with two scales, with three definitely, but with two and you can't decide which of the three sets of three to take after the first weighing, unless the two sets you weigh are of identical weight... Hmmm...
Put the stones in groups of 3. Weigh them. If their both exact put 2 of the 3rd group on one side, and a stone that you know is the correct weight of the other.
the side........ nvm my way of thinking would need a 3rd scale... your all corret in my book
