18. My little brother has a 4-digit bike lock with the digits 0-9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6-3-4-8. Which of the following can not be the correct combination of my brother's lock. Ok so this is one of those elimination problems we have to work through each answer to solve this. And for the purpose of this I want everyone to see that if we add 1 to each x to each digit that's equivalent to subtracting 10-x from each digit. So for example if we add 1 to 8-5-6-0 we get 9-6-7-1 that's also the same as subtracting 9 from all of this. So if we subtract 9 from 8 we also end up at 1. It's simply just turning this dial 9 times in the opposite direction. So what we can do is we can just only consider this in terms of addition. If we have the combination 6-3-4-8 in order to get to 8-5-6-0 we add 2 to 6, 2 to 3, 2 to 4, 8 plus 2 is in this case 0. So all of those are plus 2. In B we also add 7-7-7-7 again this is super similar over here you could also just subtract 3 for all of these but in this case we're just going to stick with addition. In C however we see that 6 plus 8 gives us this 4, 3 plus 6 gives us 9, 4 plus 6 gives us a 0, and 8 plus 8 is what's going to give us a 6. So we have some differences in C. D it's just 6 plus 5 is 1, 3 plus 5 is 8, 4 plus 5 is 9, 8 plus 3 is 3, and then E is just a plus 4. Again I'd like to reiterate that when I say 8 plus 4 is or when I say things like 8 plus 5 is 3 that really is just that if you turn 5 more after 8 we get to the 3. The tens place doesn't matter here. And as we see the only one where there's some variation is in C so C cannot be the correct combination of my brother's flock and the answer is thus C.

bike lock combination

uniform increments

current combination

inconsistent pattern

option analysis