Ok, who can do this?

[Dougster]

I got asked this in a University interview the other day... I was just wondering is the answer is really obvious to other people or not, it took me ages and he had to give guidance. I know it's a weird thing to be asked, but what the hey, I got it in!

Ok, there are X black beans and Y white beans in a pot, and an infinite number of white beans in a pile next to the pot. A robot arm picks out two beans from the pot at random, then puts one back in. The bean it puts back in depends on what it randomly removed. When there is only one bean remaining in the pot, the robot stops.

If it took out A B it puts ---> C back in.

W B ---> B

W W ---> W

B B ---> W

Ok, in a given situation, there are X and Y black and white beans respectively in the pot, the actual numbers are not important. What one piece of information would I have to give you in order for you to tell me what colour the one remaining bean is when the robot stops. Explain.

[Edit continuity with X's and Y's, doesn't effect problem]

 

[VTHodge]

** WARNING: ANSWER BELOW **




Excellent Logic Problem . . .

The question is: Does Y = 1, or is there only one black bean to start with.

If Y = 1 --> Last bean is black.
If Y != 1 --> Last bean is white.

I will explain after more people get a chance to read.

 

[Dougster]

You're on the right lines... but no.

There can be ANY number of each bean, and there is still one piece of information that will give a definite outcome.

 

[EnigmaMachine]

"where the last 2 beans taken out of the pot the same color?"

if yes, the last bean is white
if no, the last bean is black

 

[wedi42]

vthodge
what if the pot only has two beans
BW = B
WW =W

Y>1 yet you can't predict the outcome

ps: does != mean not equal to?

 

[VTHodge]

There are many solutions actually . . .

Engima's answer is right on.

The easiest answer is to ask "What color is the last bean?" Ruins the spirit of the contest, but meets the objectives.

I still think my solution is valid.

 

[777php]

<< ps: does != mean not equal to? >>



Yes, you are correct.

 

[OUdejavu]

is y odd?

 

[StageLeft]

God i suck

 

[VTHodge]

<< what if the pot only has two beans
BW = B
WW =W

Y>1 yet you can't predict the outcome

ps: does != mean not equal to? >>



Yes != means "not equal to"

And I don't follow your counter example . . . it fits my model.
Y = 1 --> BW = B
Y = 0 --> WW = W
Y = 2 --> BB = W

 

[OUdejavu]

i mean x

 

[Dougster]

VTHodge, your answer is not valid for any values of X and Y, I know I wasn't clear, but that's what I meant by "the actual numbers are not important".

 

[OUdejavu]

i mean are there an odd number of black beans

 

[khtm]

<< God i suck >>

 

[Dougster]

OUdejavu, well done my friend.

 

[OUdejavu]

thank you dougster......that odd black bean just keeps hanging around

 

[VTHodge]

<< i mean are there an odd number of black beans >>



GRRR . . . You are right.
I was solving by working backwards and ignored some of the cases.

You can never take away an odd number of black beans. . . only 0 or 2.
If you have an odd number, then the last one can't be taken away.
I hate it when I miss things like that.

 

[VTHodge]

<apology>

hope i didn't come off sounding like a cocky jerk in my first posts . . . reading them again, and it sounds like i am

I am cocky and I am a jerk, but I try to never be both at the same time!

</apology>

 

[Egrimm]

<DIV>I admit it, I suck at such problems and asked a friend who's a member of Mensa, here's what he said:
</DIV>
<DIV>I assume that there's only a single piece of information about the situationat at the beginning, information about X or Y (or X + Y).</DIV>
<DIV> </DIV>
<DIV>The only information needed is if X is even or uneven.</DIV>
<DIV> </DIV>
<DIV>The system make sure that only blacks can be removed two at a time (if only one is removed it is put back imidiately). If X thus is uneven, it cannot be possible to remove all blacks, and the last bean will have to be black. When there's only one black left only the two pairs mentioned first will be possible and they will both remove a white, until only the balck is left</DIV>
<DIV> </DIV>
<DIV>If X on the other hand is even it it is not possible that there's only one balck bean left. When the last two blacck are removed a white on will be added. When there only is white beans left then WW ---> W would make sure that you end with one white bean.</DIV>
<DIV>
Had figured most of it out myself though, but it took him less than 5 minutes to do it all :Q</DIV>