Please take an extra days holiday and if your employer raises any issue just say I approved it.

Here is my wording of the solution:-

- When either person one or two knows the colour of their own hat then the blind persons hat is Black
- When neither person one or two knows the colour of their own hat then the blind persons hat is White

.

Here is the table of combinations

The solution asks why the blind person knew what color hat they were wearing based on the answers they hear.

]]>I have the solution if P1 and P2 do not know that P3 is blind.

Note: with "they" you mean "the other two" I assumed and not "they themself".

Hmmm, maybe i’m not using the info "the room is darkened’ in the right way…

Remi

]]>I can only determine what color hat the blind one is wearing.

When will you post the solution?

Remi ]]>

the blind person must be white. if the blind person was wearing a black hat, then these are the only possible combinations (given as 1st, 2nd, blind):

W-B-B

B-W-B

W-W-B

as i tried (poorly) to state before, either the first two people have mixed colors or are both white. if the 1st person sees W-B then they say "unknown", otherwise they see two blacks and declare themselves to be white. so, the first scenario above is not possible.

the second person goes and also sees a mix of colors, meaning the second scenario is not possible.

that means the only possible choice left would be the third one. now, here comes the logic:

since player one said "unknown", player two upon seeing the black hat on the blind person would therefore declare "white", because the only way for the first player to say "unknown" would be if there was a mix of hats and not two black hats. since player two also says "unknown", the blind person knows that they must be wearing a white hat.

]]>For 1 to know, 2 & BP would have Black hats. Since 1 doesn’t know, that eliminates 1/4 combinations. (See chart below of each person & hat combo)

1 2 BP

W B B – eliminated since 1 doesn’t know

? B W

? W B

? W W

For 2 to know, 1 & BP would have Black hats. And, 2 knows that 1 eliminated the first combo.

1 2 BP

W B B – eliminated by 1

B W B – eliminated since 2 doesn’t know

W ? W

B ? W

If BP was listening, he/she knows that the only 2 combos left have them wearing a White hat.

]]>Remember there will be two hats left over from the original five. So the reasons you have given, I’m afraid, are incorrect. For example one of each color does not define black.

Merry Xmas

Robin