Sam and Alex then had the following conversation:
Alex: I don't know your number.
Sam: I don't know your number, either.
Alex: Now I know!
How many such sets of numbers can you find? Can you find all the sets which could have been thought up by the Math teacher?
7 comments:
i have a querry.
Do the students know that the nos are in range 1-10 and are consecutive.
i think that this is obvious otherwise the question makes no sense.
I think there are only two possible solutions to this problem
1)Alex given number "2"
Then Sam must have got 1 or 3
It cant be 1 otherwise he would have known Alex's number. He says "I don't know." This enables Alex to know that Sam's number is 3.
2)Alex given number 9.
similar explanation.
Sam gets 8.
Thus by my view there are tow sets of numbers:
(2,3)
(9,8)
Yes, Sam and Alex know that they have been given 2 consecutive numbers in the range 1-10. Any more answers? The puzzle is not closed as yet! Any more sets of numbers, anyone?
I have posted the solution of "The same puzzle" (1/x+1/y=1/12).
You may have a look
There are two more sets of numbers which are possible, making the total number of sets 4.
Well the two other possibilities are 3,4 and 8,7.
Lets say Alex has no. 3.
possibilities for sam 2 or 4.
Therefore alex doesnt know the no.
Now lets say that sam has no. 2.
the possibilities for Alex are 1 and 3. but if alex had 1 he wud hav known Sam's no which he didnt so Sam can make out that alex must have had no. 3.
But Sam says that he doesnt know the answer.
Now Alex knows that if Sam had no. 2 he wud have known the answer so now he knows that Sam has no. 4.
same logic goes for 8 and 7.
Sajal and Shikar will get part marks as both are right.
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