What does the fourth number refer to here？ [closed]

Solution 1:

It says that "he can’t remember the position of those numbers, and he does not know which one of the 0-9 is the fourth number".

It would be perverse for that to mean that he knows that those three numbers occur among first three positions, and so that number he can't remember must be fourth in the sequence.

The normal reading is "He can remember three of the numbers, but not the fourth", saying nothing at all about position of the number he can't remember.

Solution 2:

Fun question. The logic of this turned out a little longer than I expected. Here goes:

The whole statement only refers to four numbers that occur on a bike lock. It provides no other information whatsoever about the position of any of these numbers.

"0-9" is the range of integer numbers from 0 to 9, so "which one of the 0-9 is the fourth number" refers to a number that exists in the set of numbers {0,1,2,3,4,5,6,7,8,9}.

We read that 1,4 and 6 each occur once, in unknown positions. That leaves the fourth number to come from the reduced set {0,2,3,5,7,8,9}. Its position too is unknown.

"can’t remember the position of those numbers" refers to the unknown positions of {1,4,6} in the lock.

"the fourth number" refers unequivocally to a number, to be understood as a number from the reduced set {0,2,3,5,7,8,9}. Being a number, it is not a position. Call it X.

X might happen to be the number in the fourth position (it has a 1/4 chance of being there) but we don't know any of the positions, so we cannot with certainty refer to X as being the number in the fourth position; it may be in any of the other three.

X must therefore be understood as the fourth number under consideration in the lock set {1,4,6,X}.