Grades 5-6 Video Solutions 2022-2022_5-6

Video Transcription

Question number 23. To unlock this lock, you get the following four hints. What is the correct code for the lock?  The first one is 682, and we know that one of these digits is correct and in the right place.  The second one is 614, and this hint is one of these digits is correct but in the wrong place. The third lock is 206. Two of these digits are correct but in the wrong place.  The fourth lock is 738, and we're told that all of these digits are incorrect.  Okay, so from figure 4, we know that the digits 7, 3, 8 are not used anywhere at all. So from there, we can move on to figure 1.  Looking at figure 1, we know that 8 cannot be used, so the correct digit must then be either the 2 or the 6. And that digit has to be both correct and in the right place.  So, what if the correct digit is the 6? Well, if the correct digit is 6, then the 6 is in the same position over here.  And that would mean that this statement over here, one of these digits is correct but in the wrong place, would be false.  And that means, which again is contradictory, so the 6 cannot be in the right position.  So that means the 2 has to be in the right position, and since we're not told that any of these two values are correct, we can say that 6 is not going to be a part of the code.  Now we move on to figure 3. So in figure 3, we know that the 2 is definitely used, but we also know that it's in the wrong place as is given here.  And we also know that the 6 is not used from figure 1, so 0 is another correct digit, but 0 is not in the middle of the code. So what do we know right now?  Right now we know that the 0 is present, and we know that the 2 is also present in the third spot.  Since the third spot is already taken, and 0 is not in the middle, we know that 0 has to be the first digit of the code. So now we only have the middle spot open.  So one of these digits is correct but in the wrong place. If the 1 is the correct digit, then the 1 can also not be in the middle because the middle is the last place for it to be.  If it were correct, then it would not be in the wrong place, which would be contradictory.  So that means, and again we already know that 6 is kind of crossed out, so 4 is the last remaining option.  So only the 4 could be in the middle, it could be a correct digit and also in the wrong place.  And that tells us that our final number is 042, and that means that our answer choice is D.

Video Summary

The correct code for the lock, based on the given hints, is 042. The process involves deducing that digits 7, 3, 8 are unused, 6 is not in the correct place, and 0 is a correct digit but not in the middle. This leads to placing 0 at the start and ensuring 2 is in the third position. From hint two, the only possible correct digit for the middle is 4, as the other options (1 and 6) either contradict previous information or are eliminated. Thus, the lock code is 042, corresponding to answer choice D.

Keywords

lock code

deduction

digits

hints

solution