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.

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:

black...everytime!

No its white evry time...

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

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

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