3 red and 2 white roses

Reply Sun 10 Feb, 2008 04:01 am
I have 3 red and 2 white roses. I ask my three sisters to stand one behind the other and ask them to close their eyes. Then I place one flower on each head and put the balance two in my packet. They open their eyes simultaneously. The last can see the heads the elder two sisters at her front. The middle sister in the middle can see the head of the eldest only. The eldest in front cannot see the heads of the other two behind her.
When asked my sister in the LAST says she does not know the colour of her flower. Then the middle sister also gives the same reply. however my first sister replies correctly How?
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Reply Sun 10 Feb, 2008 04:51 am
(front) s1 s2 s3 (back)

S3 can see S2 and S1. S2 can see S1 only. S1 sees nobody of course.

S3 can see the flowers of S2 and S1.

The only way S3 will know her own colour is if she sees two white roses in front of her. S2 and S1 understand this. If S3 knows her own colour (red) and names it, then at once S2 and S1 will know theirs also.

But she does not, evidently. Therefore S2 knows that her own colour could be either white or red. She can see S1's rose. If it is white, she knows that her own rose cannot also be white. Therefore she would know that her own rose is red. But she answers that she does not know the colour of her own rose.

Therefore S1 knows that her own rose cannot be white.

does not know t
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Reply Sun 10 Feb, 2008 02:01 pm
Here's one I just made up:

There are seven sisters (s0-s6) in line as before (s6 at the front, s0 at the back).
There are nine roses: 1 white, 2 yellow, 3 orange, 3 red.

As before, starting from the back, a sister will state the color of her rose if she knows it.

Sisters 0, 1, ... can't determine the color of their roses. However sister N can. What is the largest possible value for N, and how does she know what color her rose is?

In other words, what is the maximum number of consecutive sisters (starting with s0) who don't know what color their rose is?

I numbered the sisters so that the answers to these two questions is the same number.

If this question were applied to Whim's problem, the answer would be 2 because the third sister (s2 using my notation) is guaranteed to have enough information to determine the color of her rose.
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