Our Monkeying Days...

Tuesday, July 25, 2006

Got challenged with several maths brainteasers by xiu today, so shall share them here for all those who, like me, feel like they need to get their rusty brains up and running again before uni starts. :P

Qn 1: You have 5 hats, 3 green hats and 2 red hats. 3 people are standing facing the wall, and you place one hat on each of their heads. The 3 people are then told to turn 90 degrees to the right, such that the person at the back can see the colours of the hats on the first 2 ppl, and the middle person can see the hat on the person right in front. You ask the person at the back whether he knows the colour of the hat on his head, and the person says, 'no'. You then ask the person in the middle whether he knows the colour of the hat on his head, and he too replies, 'no'. Finally, you ask the person in front if he knows the colour of his hat, and this time, he says, 'yes'. So what IS the colour of the hat on the person right in front?

Qn 2:
Scenerio 1 (easy): You have 8 stones, of which 7 are of the same weight, and 1 is heavier than the rest, and a balancing scale (aka you can put stones on each side of the scale to see if they balance). How can you figure out which stone is the odd one out in 3 steps? (You can put as many stones as you like on each side of the scale in each of the steps)

Scenerio 2 (medium): This time, you have 9 stones, of which 1 is the odd one out. However, now you are not told if this stone is heavier or lighter than the rest. How can you figure out which stone is the odd one out, and whether it is lighter or heavier than the other stones, in 3 steps?

Scenerio 3 (difficult): You now have 12 stones. As with scenario 2, you are not told if the stone that is the odd one out is heavier or lighter than the rest. Figure out which stone is of different weight, and whether it is heavier or lighter, in 3 steps.

Qn 3: (this qn is madness...I couldn’t solve it...But oh wells, I know there are geniuses out that who can probably like get it the moment they look at it :P):
100 people are stranded on an island, of which 50 are brown-eyed, while 50 are blue-eyed. However, these 100 people are not informed of the ratio of brown-eyed people vs blue-eyed people, and are only told of one thing, that there is at least 1 blue-eyed person amongst the 100 of them. Every day, a ship will arrive on the island to fetch the blue-eyed people back to the mainland. So if a person is sure that he or she is blue-eyed, he or she can board the ship. Therefore, how many days does it take for all the blue-eyed people to figure out the colour of their eyes (assuming they’ve never stared in a mirror before in their whole lives and therefore are clueless about what colour their eyes are) and to leave the island, assuming that all 100 people on the island are not allowed to communicate with each other, and are only allowed to observe the colour of the eyes of other people stranded there. (The first day the people are stranded on the island is taken to be day 0)

-XL :)

P.s Xiu is posting up embarrassing photos of me from our outing later today. Hmmm I should prepare to go into hiding...:P
P.p.s Ans for the qn. 1) green 2) err the explanation for this qn takes too long to type, so just ask xiufang or me if you want to find out the ans :P 3) 50 days (again the explanation is quite complex, so just find either of us :P)

~*2:43 PM*~

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