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Marbles

Puzzle:

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?

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Solution:

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 it's own.



4 comments:

prashant said...

black...everytime!

Parwez said...

No its white evry time...

Anonymous said...

i m rajesh
yes it is white every time
thr r 13 white n 15 black initially
consider 2 cases
case 1:
take 2 whites every time n replace with a black as they r of same colour.then u ll have
1w n 21b
u always take 2 blacks now and u replace it with 1 black as they r of d same colour
then 1w n 11b become
1w n 6b doing it again
1w n 3b
1w n 2b
1w n 1b
finally u ll take 1w n 1b which r of different color n replace with white.so d colour of the last ball is white
case 2:
every time u take 2 balls assume they r of different colours.then replace them with 1 white ball
initially 13w n 15b
take out 13 times 1w n 1b n each time u add 1w.then u ll have
13w n 2b
take 2 times 1w n 1b then
13w n 0b
take 2 whites every time and add a black
1w n 6b take 2 blacks n add a black
1w n 3b take 2 blacks
1w n 2b take 2 blacks
1w n 1b take 1 black n 1white.as these r of different colour replace them with a white.
here also d last ball is white


so in each case last ball is white

Akhilesh said...

it it simple the answer is white alwys

as the only option fr white to b out of the box is to b in pairs

and white is odd

and no white is replaced in the whoel processes

o the other hand
black is replaced nd it also has an option of cmng out when its only black nd white




so its alwys white