Consider the following example:
Three boys- Ashish, Bhanu and Chintu replied to the question, "Who among you is a Doctor?" in the following manner:
We know that exactly one of these boys is a Doctor, one is a Painter and one is an Athlete. Also, one of them always speaks the truth, one always lies and one alternates between the truth and the lie.
| Ashish: |
Bhanu: |
Chintu: |
| I am a Doctor |
Chintu is an Athlete |
I am not a Painter |
| Bhanu is a Painter |
Ashish is not a Doctor |
Bhanu is not a painter |
| I am a Switcher |
I am a Lie-teller |
Ashish is a Lie-teller |
In the above question, Bhanu makes the statement, “I am a Lie-teller”, which implies that Bhanu is a Switcher. Also, Ashish said that he is a Switcher, which implies that he can be either a Lie-teller or a Switcher. Now, since Bhanu is the Switcher, Ashish is definitely the Lie-teller. This leaves us with Chintu as the Truth-Speaker. Since Bhanu is the Switcher, so the statements following/preceding the statement, “I am a Lie-teller” are true, we can conclude that Ashish is not a Doctor. Also as Chintu is a Truth-Speaker, according to his statements, Bhanu is not a painter and he himself is not a painter, thus Ashish is the painter. Now, Bhanu’s first statement is a lie (since third statement is also a lie, so the order for Bhanu’s statements will be 1st-false,2nd-true,3rd-false). This means Chintu is not an athlete, which leaves us with the only option for Chintu as Doctor and Bhanu as an athlete.
| Ashish |
Bhanu |
Chintu |
| Lie-teller |
Switcher |
Truth-Speaker |
| Painter |
Athlete |
Doctor |
Therefore, the answer to the question, ‘Who is a Doctor’, is Chintu.
If we consider the statement like “I am a Truth-Speaker it is not of much use as truth speaker, lie teller and switcher all three can give this statement.
Step 2: Now what if we do not have any of the above said 4 statements in any of the statements. In that case we will self assume their status and the assumption in which there is no contradiction will be the answer.
Now, consider the following example:
Uday, Ramesh and Suresh made the following statements regarding the type of vehicle they own. Each one of them belongs to one category of Truth-Speaker, Lie-teller or Switcher. Only one among them is a Truth-Speaker. Further, each of them own a different vehicle and each of them own exactly one among car, cycle and bike.
| Uday |
Ramesh |
Suresh |
| Suresh does not own a car |
Uday does not own a bike |
Uday is a Lie-teller |
| I am not an Switcher |
I am not a Lie-teller |
Ramesh is a Truth-Speaker |
| Ramesh does not own a car |
Suresh does not own a cycle |
I own a cycle |
SOLUTION: The most important information is there is only one Truth-Speaker:
Now we will proceed as follows:
- As Uday says” I am not a Switcher”. As discussed above he can be a truth speaker or a switcher.
- now we will proceed with self assumption method
(a)Let us first assume that he is a truth speaker
So,all his statements are true. So he will own a car as per his first and third statement neither of Ramesh or Suresh owns a car.
Now Ramesh’s last statement is true. So he can be a switcher or a truth speaker. Now since he cannot be a truth speaker (as only one truth speaker is there), he must be a switcher. So his second statement must be false. But it is true. So our assumption is wrong.
(b)Let us now take the second assumption that Uday is a Switcher.
So his second statement is false. So first and third are true. This proved that Uday owns a car.
Now see that last column of Suresh’s statements. His first statement is false. So he must be a lie teller or switcher.
Now it is given that there is exactly one truth speaker and now the only one person left is Ramesh. So he is a truth speaker. so we can conclude that his all three statements are true.
As per his last statement “Suresh does not own a cycle”, we can conclude that Suresh owns a bike.
So we can now check that Suresh’s first and last statement is false and second statement is true .So he is a switcher. So we can conclude the following:
| Uday |
Ramesh |
Suresh |
| Switcher |
Truth-Speaker |
Switcher |
| Car |
Cycle |
Bike |
So, there are 2 Switchers and 1 Truth-Speaker.