Once there was a king who wanted to find out how intelligent his 3 chief advisors (AD1, AD2, AD3) were. So he called them and started a game with them. He wrote a number on the back of each of the advisors and asked them to guess what number was written on their own back.
The rules of the game are :
- The advisors have no way of seeing the number written on their own back.
- They can see the numbers written on the other advisors' backs.
- No communication is allowed between the advisors.
- All the three numbers are integers and are greater than or equal to 40
- AD1, AD2, AD3 have integers which are in strictly increasing order.
Five minutes after telling them about the rules, the king asked all the advisors whether they knew what number was written on their back. All of them replied "I don't know".
After five more minutes, the king asked the same question again. This time AD1 and AD2 replied "I know" but AD3 still replied "I don't know".
After five more minutes, the king repeated his question. This time, all of the advisors replied "I know".
Are YOU intelligent enough to figure out what were the numbers written on the back of each of the advisors ?
Happy solving :)
Cheers !
P.S : Please DON'T post your solutions as comments on this post. Mail them to me at : harshgupta1987@gmail.com. I will post the solution on the blog after 1 week.
can we have the answers now..???
ReplyDeleteAnswer :
ReplyDeleteAD1 - 40, AD2 - 42, AD3 - 43
Solution :
Now, its given that the numbers assigned to AD1, AD2, AD3 are in strictly increasing order.
AD1's thinking - AD1 sees that AD2 and AD3 have the numbers 42 and 43 respectively. Therefore, he can logically conclude that he either has 40 or 41. But at the moment he cant be sure which one of the two is it. So when asked for the first time, he replies "I dont know"
AD2's thinking - AD2 sees that AD1 and AD3 have the numbers 40 and 43 respectively. Therefore, he concludes that he either has 41 or 42, but he cant be sure. So, he replies "I dont know"
AD3's thinking - AD3 sees that AD1 and AD2 have 40 and 42 respectively. Therefore, he concludes that his number can be any integer greater than or equal to 43. So, he too replies "I dont know"
Thus, when the king asks for the 1st time, all the advisors reply "I dont know"
Now, after all the advisors have replied for the first time :
AD1 thinks - I was confused between 40 and 41. But if I had 41, then AD2 would not have been confused about his number. So, I must have 40. So, he replied "I know"
AD2 thinks - I was confused between 41 and 42. But if I had 41, then AD1 would not have been confused about his number. So, I must have 42. So, he replied "I know"
AD3 is still confused. SO, he replies "I dont know"
Now, after hearing that AD1 and AD2 have corretcly identified their numbers, after only 2 tries, AD3 concludes that it is only possible if his own number is 43. Thus, the third time, he too replies "I know" ...
So now .... you all know too ! :)
Cheers !