[Guest]

An old farmer, as inheritance, was going to divide his properties (lands) into his 3 daughters (the oldest, the youngest and the “middle one”). He had a total of X properties. All of the three girls knew the value of X. All of them were going to have a different amount and an integer number of lands. The oldest wins more lands then the middle, and the middle wins more lands than the youngest. Each girl knows how many properties she´s going to win, but doesn´t know about the sisters. The father don´t allow them to communicate with each other. Starting a game (because he knew all 3 were very smart) he brings all sisters together and asks to the oldest:

“How many properties are your sisters winning?”

“I don’t know dad.” – She answered.

“How many properties are your sisters winning?” – He asked to the middle sister this time.

“I don’t know dad.” – She answered too.

“How many properties are your sisters winning?” – He asked to the youngest sister.

“I don’t know dad.” – Was the answered again.

He asks the same questions again, in the same order. On the seventh question, directed to the oldest, she answered; “Yes, now I know.”

Knowing the youngest have to win a minimum of 1 property and the oldest a maximum of 10 properties, how many lands each girl wins? And how the oldest figure it out?

[Shakeepuddn]

Because the farmer keeps repeating the question, I assume he is giving the girls the clue that there is only one obvious solution. If only one solution it would have to be 3 to the oldest, 2 to the middle and one to the youngest for a total of 6.

Hmmm. This actually belongs in the logic forum but I'll take a stab.

[Guest]

There are 13 properties. If the max the oldest can have is 10 and the minimum the youngest can have is 1, and the middle has 2, that is 13 total. If there were more than 13, the oldest could have more than 10 and there can not be less than 13.

The youngest can not have more than 3, since 4+5+6=15, which is too many properties.

The oldest can not have fewer than 6, since 5+4+3=12, too few properties.

The middle must have between 2 and 5 properties. 2 if the others are 1 and 10, 5 if the others are 1 and 7.

On the first question, the oldest did not know. If she had 10, she would have known it was 1 and 2. If she had 9 she would have known it was 1 and 3. Therefore she has between 6 and 8.

On the second question, she did not know. She can not have 2. If she had 3, she would know answer was 8 and 2. She would not know the answer if she had 4,5.

The youngest did not know. If she had 3, she would have known the others were 4 and 6. If she had 1 or 2, she would not know.

After first round, ranges for oldest to youngest are 6 to 8, 4 or 5, 1 or 2.

In 2nd round:

Oldest did not know. If she had 8, she would know it was 4 and 1. If she had 6, she would know it was 2 and 5. If she has 7, then she would not know, so she has 7.

2nd knows this, but does not know how many the youngest has? She has to know the oldest has 7, so the youngest has 6 minus whatever the middle has.

Something is not right.

[Guest]

I feel there are 19 properties. We can have these combinations for 19: (10+8+1; 10+7+2; 10+6+3; 10+5+4; 9+8+2; 9+7+3; 9+6+4; 8+7+4; 8+6+5).

Q1> Oldest sister (O) doesn’t guess which means she has 10 or 9 or 8. Left combinations are now (10+8+1; 10+7+2; 10+6+3; 10+5+4; 9+8+2; 9+7+3; 9+6+4; 8+7+4; 8+6+5).

Q2> Middle sister (M) doesn’t guess which means she has 8 or 7 or 6. Left combinations are now (10+8+1; 10+7+2; 10+6+3; 9+8+2; 9+7+3; 9+6+4; 8+7+4; 8+6+5).

Q3> Youngest sister (Y) doesn’t guess which means she has 4 or 3 or 2. Left combinations are (10+7+2; 10+6+3; 9+8+2; 9+7+3; 9+6+4; 8+7+4).

Q4> Now again O can’t guess which means she has 10 or 9. Left combinations are (10+7+2; 10+6+3; 9+8+2; 9+7+3; 9+6+4).

Q5> M doesn’t guess in second attempt means she has 7 or 6. Left combinations are (10+7+2; 10+6+3; 9+7+3; 9+6+4).

Q6> Now Y doesn’t guess in second attempt means she has 3. Left combinations are (10+6+3; 9+7+3).

Q7> Now O can guess in her third attempt between (10+6+3 and 9+7+3) depending on she has 10 or 9. This is the seventh question overall.

[Guest]

I agree with swapnil. I don't have a better way to figure it out, I did it by process of elimination starting with the 120 combinations that match the rules.