An Unexpected Trick
There was a logic master and his pupil, who were playing a new game called The Dead Giveaway.
The logic master told his pupil the rules, "Here on the table is a special deck with 4 red cards and 3 black ones. Shuffle the cards and draw them 1 by 1. If you draw a red card, I'll give you half of your money, but if you draw a black one, you'll give me half of your money."
The pupil sees there is 1 more red card than black, so he agrees to the rules and plays the game. After all 7 cards were drawn, the pupil realized he ended up with lesser money than before! Shocked, he told his master about this, but he replied with a smile.
Why did the pupil lose some of his money? And if he started with $100, how much was he left with?
posted by C at
12:27 AM
8 Comments:
It's a bit unclear. If he draws red card he is given half of his own money?
Does this mean that if he starts with $100 then he will be given $50 of his own money so that he will still have just $100 dollars.
If this is the case then that is defiantly the reason he will not gain money. And he will end up with $12.50
Otherwise it has to do with the reasoning that when he loses money he loses half. But when he gains money he does not double it, he adds 1/2.
So 4 red card is 1.5*1.5*1.5*1.5
and 3 black cards is 0.5*0.5*0.5
If I'm processing this correctly in my mind then. Multiplication is commutative therefore it doesn't matter the order the cards are drawn.
100*(1.5)^4*(0.5)^3 = $63.28125
For eg: He has $100 so he is given 1/2 x $100 = $50.
Neal, you got the right answer... I was hoping this question's answer will require a few days of thinking.
A: $63.28125 round off to $63.28
hi C...the people here are good at this stuff...not too many questions last for more than 24 hours...one of my lasted for a whole 4 minutes!(yeah,i'm looking at you Cam) ;[
Let A be the value he started with, B what he ended with.
A x (1.50^4) x (1/8)
1.5 being what he gets from a red multiplied raised to the fourth power because there are 4 red cards.
1/8 because its 1/2 multiplied by itself 3 times.
1.5 ^4 = 5.0625
So A x 5.0625 x 1/8 = final value.
5.0625 x 1/8 =~5/8
That, of course, being smaller than one, therefore lowering the value it is multiplied by.
Another bit worth mentioning is the order. He is, of course, not going to draw 4 reds then 4 blacks as the above scenario plays out. no matter. order does not matter in multiplication.
example: 3 x 2 x 5 = 5 x 2 x 3
so even if he draws a black then red, he will STILL end up multiplying by 5/8. no matter what order, he SHOULD (unless I skrewed up somewhere -.-) get the same value.
-Soli
Oops! so busy working it out I never posted the final value.
It is 100 x (5.0625 / 8) which = 63.28125.
Moral of the story? never play games with logic masters ^.^
hey Soli...good post
He will end up wid $63.28125
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