Each of the 88 people living in a town has at least one friend.
Of these people, 44 are honest and always truthful, and 44 are liars and always lie.
When the Governor visited the town, 44 of the people in the town told him, "All my friends are honest", and 44 of them said, "All my friends are liars."
According to this, what is the minimum number of pairs of friends consisting of one honest person and one dishonest person that live in the town? Explain.
Solution to the Problem:
There must be at least one pair of friends where one is honest and one is a liar.
Let H stand for an honest person and L stand for a Liar.
My first reaction was to say that the minimum was 22:
11 pairs of HH
22 pairs of HL
11 pairs of LL
However, the key to the problem is the phrase "at least one friend."
So, the answer would be that there must be at least ONE pair of HL.
1 group of 42 friends: H LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
1 pair: HL
1 pair: LL
1 group of 42 friends: HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
In the first group, all 42 would answer yes "All my friends are liars."
In the HL pair, 2 would answer, "All my friends are liars."
In the LL pair, 2 would answer, "All my friends are honest."
In the last group, all 42 would answer, "all my friends are honest."
However, Colin Bowey sent in a solution in which the answer would be zero, and I accepted that.
Click here for his possible formations of friends
I deccided to accept the answers of 0, 1, and 22 for this problem.
Let H stand for an honest person and L stand for a Liar.
My first reaction was to say that the minimum was 22:
11 pairs of HH
22 pairs of HL
11 pairs of LL
However, the key to the problem is the phrase "at least one friend."
So, the answer would be that there must be at least ONE pair of HL.
1 group of 42 friends: H LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
1 pair: HL
1 pair: LL
1 group of 42 friends: HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
In the first group, all 42 would answer yes "All my friends are liars."
In the HL pair, 2 would answer, "All my friends are liars."
In the LL pair, 2 would answer, "All my friends are honest."
In the last group, all 42 would answer, "all my friends are honest."
However, Colin Bowey sent in a solution in which the answer would be zero, and I accepted that.
Click here for his possible formations of friends
I deccided to accept the answers of 0, 1, and 22 for this problem.
Correctly solved by:
| 1. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 2. Ritwik Chaudhuri | Santiniketan, West Bengal, India |
| 3. Kelly Stubblefield | Mobile, Alabama |
| 4. Ivy Joseph | Pune, Maharashtra, India |
| 5. Veena Mg | Bangalore, Karnataka, India |