Braingle: 'Marble and Box' Brain Teaser

Marble and Box

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Puzzle ID:	#11079
Fun:	(2.72)
Difficulty:	(1.72)
Category:	Probability
Submitted By:	electronjohn
Corrected By:	boodler

In a box you have 13 white marbles and 15 black marbles. You also have 28 black marbles outside the box. Remove two marbles, randomly, from the box. If they are of different colors, put the white one back in the box. If they are the same color, take them out and put a black marble back in the box. Continue this until only one marble remains in the box. What color is the last marble?

Answer

The last marble will be WHITE.

Since marbles can only be taken out in pairs and you started off with an odd number of whites there is always going to be one white left over that you'll keep putting back in the box until it's left on its own.
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Comments

PhilDunphy Mar 20, 2003	This was easy after the last one I tried which was something to do with cats thinking they were dogs, and I really need to lie down now
im_para_noid Mar 20, 2003	Okay, I am a little confused, what would happen if you take out the first twelve marbles, and they each happen to be white, so you add the 6 black ones to the box...but then, on your next pick, you get a white and a black one, and then you add another black marble into the box, now you would be out of white marbles...I don't think this situation would occur very often, but wouldn't you be out of white marbles then?
Skellum Mar 21, 2003	im_para_noid, the rules of the game state "If they are of different colors, put the white one back... " so you can never run out of white marbles.
Rosey27 Apr 03, 2003	im_para_noid um in good intention why are you paranoid? : )
Pheonix_down Apr 10, 2003	Great teaser! I actually got it!
Skybet Nov 09, 2004	Fun but pretty simple
yayayaa Mar 06, 2005	I think that is pretty cool! did a friend tell you taht or did you make it up yourself? i'm new so i'll probably think everything is "COOL"
krabcat Mar 06, 2005	i think i knbow exectly y i dident gett it iv been up exactly(give or take a litle for mestkes) 23 hours 48 min.
wildmistyblue Mar 06, 2005	Cool teaser!
greebmaster-1 Mar 06, 2005	man, that's weird. not my kind of teaser but cool-ish
TeenDivaPrincess Mar 06, 2005	This is one of the ONLY math-related teasers that I have been able to get! Thanks for a great teaser!
Kinergy Mar 06, 2005	I liked this one. I just pretended there were 2 black and 2 white left, then tried different combinations and it kept coming up white, so that was my guess. May not be air-tight though.
CHUCKLZ Mar 06, 2005	I found this one to be very easy. When I read the directions it gave me the answer...good one though
porky Mar 06, 2005	yes i thought too that it would have been a white mrable.
freakydoughnut1 Mar 06, 2005	that sucked, i tried it and it didn't work
(user deleted) Mar 06, 2005	this one i enjoyed thourohly it made me smile.
tdg_chick Mar 06, 2005	that one was 2 easy!!
Tree Mar 06, 2005	I kept thinking there was going to be some kind of trick because it was kinda' easy.
morganik Mar 06, 2005	not bad, a little eazy but still creative.
hotcalibabe3 Mar 10, 2005	CAN U PLEEZ FREEKIN MAK UR GAY THINGZ EZIER!!!
ElectronJohn Mar 10, 2005	Hotcalibabe3, have you lost your marbles! (sorry, just could not resist) It is pretty easy as it is.
Therulerofthem Jul 16, 2005	what would happen if you took out one black and white every time and then took out the last to blacks, had to put another black back in, and its the last one?
mr_brainiac Jan 08, 2006	I didn't get it, sounded too complicated, didn't even really try, wasn't willing to put six months of thought into it ,as I the suspected it might take. The answer pointed out the one important and obvious factor that never even occurred to me, always putting the white marble back inside.
brainjuice Mar 27, 2006	i guess white and it is correct! :p
opqpop Jan 26, 2010	Good brainteaser. I was unable to immediately get the answer, had to think a bit before getting it. It helped me see that my logic skills could still use some work. I focused too much on the cases: -1 black, -2 white +1 black, and -1 black. If I complete ignored the blacks, I could have immediately got the answer, which is what I hope to achieve with more brainteaser practice.
opqpop Sep 11, 2010	lol I don't even remember this problem, but I got it instantly this time around Good to see some improvement in my logic skills.