Guessing Game

Given the first guess (HHH) has only one correct coin, there must only be one head (H) in the solution.

Therefore there are only three possibilities: HTT, THT, and TTH.

Since HTT and TTH are also guesses with only one correct coin, the solution must be THT.

As such, the answer is T H T

We can say it by trying the first row.

In first row, the answer is $HHH$ and here one guess is correct. For this, we get 3 cases.

1. If 1st H is correct, then 2nd and 3rd H are incorrect. So the correct one is $HTT$ . But it is still incorrect for the 3rd row.

2. If 2nd H is correct, then 1st and 3rd H are incorrect. So the correct one is $\boxed{THT}$ . It's the correct answer. For the accuracy we can try for 3rd cases in the same way. Then we get $TTH$ which is also incorrect.

The first guess tells us only one H in the answer The only answer with one H has to be correct

Clearly in the first two guesses, the correct coin isn't the rightmost one, so the rightmost coin is T. This coin is thus the correct one in guess 3, so the other two coins in that guess are wrong, hence THT.

Using $\color{#3D99F6} \text{C}$ for the correct coin and $\color{#D61F06}W$ for the incorrect coin.

$\begin{array} {rlll} \text{Assuming: Guess 1} & \color{#3D99F6} \text H \color{#D61F06}\text{HH} \ \small \color{#3D99F6}OK & \color{#D61F06} \text H \color{#3D99F6} \text H \color{#D61F06} \text H \ \small \color{#3D99F6}OK & \color{#D61F06} \text{HH} \color{#3D99F6} \text H \ \small \color{#3D99F6}OK \\ \text{Guess 2} & \color{#D61F06} \text T \color{#3D99F6}\text T \color{#D61F06} \text H \ \small \color{#3D99F6}OK & \color{#3D99F6} \text T \color{#D61F06}\text T \color{#D61F06} \text H \ \small \color{#3D99F6}OK & \color{#3D99F6} \text T \color{#3D99F6}\text T \color{#3D99F6} \text H \ \small \color{#D61F06}No \\ \text{Guess 3} & \color{#3D99F6} \text H \color{#3D99F6}\text T \color{#3D99F6} \text T \ \small \color{#D61F06}No & \color{#D61F06} \text H \color{#D61F06}\text T \color{#3D99F6} \text T \ \small \color{#3D99F6} OK & \color{#D61F06} \text H \color{#3D99F6}\text T \color{#D61F06} \text T \ \small \color{#3D99F6}OK \\ \hline & \small \color{#D61F06} \quad No & \boxed{\color{#3D99F6}\text{THT}} \ \small \color{#3D99F6}OK & \small \color{#D61F06} \quad No \end{array}$

With the first guess, if the one correct coin is the 3rd coin being heads, then the 2nd guess would be totally correct. So coin 3 must be tails. (I think that I noticed this because the 3rd coin is the only one that does not change in the first two guesses). So the 3rd coin is a tail. And in the 3rd guess which does have the 3rd coin as tail which is right there is only one coin correct. So the way the 3 coins are placed in the 3rd guess must be entirely wrong, other than the 3rd coin. So the coins must be arranged Tail, Head, Tail. | Another question that occurs to me is if Alice arranges the coins in ANY different arrangement, what is the maximum number of guesses required before the 'guesser' would know for sure how the coins were arranged. I'll have to ponder this one! Regards, David

But they didn't tell you that Alice is a jester.

but seriously ...

HHH - only one coin can be H.

TTH - H is not correct because if it were TT with both wrong would be HH and the first guess would have been right. So the third coin is definitely T.

HTT - the last T is correct, first two both wrong. Leaves only

THT

From the first guess we know that there is only 1 head From the second guess we know that if the head was in the right position the other two tails will be in the right place too( there are 2 ways to arrange the other 2 coins but since they are both tails the 2 combinations will be the same) We can use the same method for the 3rd guess and conclude that that is not the right position for the head coin aswell Therefore the right position for the head coin is in the middle . From there we get 2 identical combinations for the tails and we get to the right answer : THT

we will try to infer as much information we can get from each statement. OK!

now coming to statement 1 : H H H "You got only 1 coin correct."

it might be the case that first coin is at correct place therefore configuration can be , HTT ( why T T? because they had to be T T to make this statement correct.)

similarly it might be the case that * second coin is at correct place * therefore configuration is , THT

or third coin is at correct place , hence configuration is TTH

same as above,

now do the above for second statement hence possible configurations are, THT, HTT and HHH.

now do the above for third statement hence possible configurations are, HHH, TTH and THT

configuration common to all the three statement is THT.

since each person only got 1 coin correct, we must find out which side was different out of the three for instance, in the first column, it is HTH so the different one is T, ||||

Knowing only one attribute is correct with HHH and TTH we know that either there is one correct coin in the first two positions in the first two sequences OR the last coin in correct in both sequence. Because all possibilities are covered for the first two sequences in the first two positions the correct coin must be in the first two positions for the first two sequences. Because only one is correct the first two positions must be opposite. Knowing this we know that the third position is T and the first two positions are the opposite of HTT.

Consider the third coin. If it is 'H', then by the first clue, the other two are 'T'.
This possibility is contradicted by the second guess. Thus the third coin is 'T' and it is the only correct coin for the third guess. Reverse the other two coins for the third guess and we have the solution: THT. (Verify that this solution matches the answers for all three guesses.)

The first two coins in each triplet are HH, TT, and HT. To avoid getting more than one coin correct, the first two in the actual sequence must be TH. If the answer was THH, our second guess would have two correct coins. By process of elimination, the answer is THT.

After the first guess, we know that there is only one 'H' in the answer. After the second and third guess, we are shown that the 'H' is not in the third or first positions. This means that it must be in the center position, and that the other two coins must be in the 'T' position. Thus the answer is 'THT'.