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February 18, 2018, 10:51:21 AM
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: A pot of beans!  ( 4275 )
« : July 04, 2007, 11:39:53 PM From Shrinidhi»



A pot of beans!


A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.

At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?

 
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« #1 : July 21, 2007, 11:28:19 PM From spazinvader»

The bean left in the end should be a white bean.

Am i right?Reply please.
« #2 : July 21, 2007, 11:42:33 PM From Shrinidhi»

Yup, thats right. But just explain the reason as well.
« #3 : July 22, 2007, 12:26:45 AM From spazinvader»

I am trying my level best to tell it.

There are totally 75 white beans and 150 black ones.
If there should be a number less to the pot then the possible ones are
1)encountering two white beans,neglecting both and putting one black into the pot
2)encountering any,pairing with black.
By the case 2,we shall finish all the black beans by combining with just a single white bean.
Then by the case 1,we can eliminate 74 white beans and get 74 black beans.

Neglect the 74 black by the case 2.The white bean will reside in the pot until all the black beans are emptied.
Thus there will be just only one white bean in the end.

Hope i am not very clear.If so,i will explain tomm.I am not getting words properly.
« #4 : August 22, 2007, 08:24:10 PM From jason43dcruz»

Its a white as mentioned before. The reason is :

Initially there are an odd number of white beans.The only way to get rid of the white beans is two at a time so eventually we will be left with one white bean and x black beans.Now since we cant get rid of a single white bean it will remain till the end.
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