4 logicians ate up 11 pieces of fish fries but didn't notice how many each had eaten. They could discover this from a few questions and answer. Can you?
The logic puzzle
Four friends, Ani, Bonny, Chinu, and Debu were in an intensive evening discussion on whether all problems can be solved by logic. They are deeply fascinated by the subject of logic. In the process of discussion, they devoured 11 pieces of fish fry served to them.
All of them knew each of the four has eaten at least 1 piece, but they didn’t know exactly how many others ate. Playfully, they agreed to ask questions to discover what others ate. Only condition—answer to the question must not be known to the questioner.
Ani started with the first question to Bonny: Did you eat more fries than me Bonny?
Bonny: I don’t know. What about you Chinu? Did you eat more pieces than me?
Chinu: I don’t know.
Debu: Alright. I know how many each of you ate.
The other three also exclaimed together: We also know now.
Do you?
Time for you: 20 minutes.
Solution to 4 logicians and 11 fish fries logic puzzle
Before going into the questions, let us ask,
Question: What are the minimum and maximum possible four numbers?
Conclusion 1: By description of the puzzle, the minimum number for each of the four is 1.
And the maximum? The maximum can be as large as 8.
Let us ask a second probing question,
Question: What can be the least value of the maximum number for any of the four to be confident that none ate more?
This is an important question to consider.
Reasoning: If any of the four ate 6, 7 or 8, the person could be confident that he or she ate the maximum. What about 5? With 5 also, one can confidently say—I ate the maximum, because none else can eat another 5. With 4 this is not possible.
Conclusion 2: One can be confident of eating the maximum if he or she ate at least 5 fish fries.
Consequences of first question and its answer
Ani asked the first question: Did you eat more fries than me, Bonny?
If Ani herself ate 5 fries, she won’t have asked the question to Bonny. This is true because of the condition imposed on questioning at the beginning.
Conclusion 3: Ani must have eaten maximum 4 numbers of fries and minimum 1 fry.
Bonny answered to Ani’s question and asked a second question: I don’t know. What about you Chinu? Did you eat more pieces than me?
In the first part of answer, Bonny made sure that she also does not know. If her number were 5, she would have answered YES. So the maximum that she could have eaten is also 4. Repetition of Ani’s question to Chinu further confirmed that Bonny couldn’t have eaten 5.
But, let us not stop at that and consider how many ways Bonny could have answered. Bonny could also have answered with NO. If she had eaten 1 piece she would have been sure that she couldn’t have eaten more than Ani as minimum number for Ani is known as 1. Being expert in using logic, all of them knew that Ani could have eaten 1 to 4 pieces.
So,
Conclusion 4: Bonny ate minimum 2 and maximum 4 numbers of fish fries. Her number may be 2, 3 or 4.
All of them could deduce this.
Consequences of the answer to second question
Bonny asked the second question to Chinu: What about you Chinu? Did you eat more pieces than me?
Chinu replied: I don’t know.
Before making the reply, Chinu knew that the minimum and maximum for Bonny are 2 and 4. When she expressed her uncertainty, she indirectly confirmed that she also didn’t eat 5 fries. Her maximum number is also 4.
What about the minimum for Chinu? She knew that the minimum for Bonny is 2. So she would have answered NO if she ate 1 or 2. As she has expressed her uncertainty; it implies that her minimum is not 2; it is 3.
Conclusion 5: Chinu could have eaten 3 or 4 pieces.
Consequences of the confirmation of Debu
Debu keenly followed the questions and answers and declared that he knew how many each has eaten.
Debu could have been certain of numbers for all only if he ate more than 4 and knew that all others had eaten less than him.
Could he have eaten more than 5 pieces?
Let us account for the possible numbers for the first three.
Conclusion 6: Ani is the only one who could have eaten 1 piece. None else has 1 in his or her possible set of values.
Conclusion 7: Bonny could have eaten only 2 pieces. This is because, with number 1 confirmed for Ani, the value 2 is left only for Bonny.
Ani and Bonny together ate 3 pieces; 8 are left and possible number for Chinu is 3 or 4.
Conclusion 8: Chinu could have eaten only 3 pieces out of 8 left, not 4 because minimum number for Debu is 5.
Final conclusion: The rest 5 pieces must have been gobbled up fast by Debu.
Breakup of number of fish fries the four ate,
Ani: 1, Bonny: 2, Chinu: 3 and Debu: 5. Total 11.
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