Logic game one. The scenario here provides us with a lot less information than we normally expect. The only thing we can get from it is that we're making five-digit codes. So we're gonna have five spaces, we should number them 1 through 5. Each of the first two rules tell us something that we normally find out in the scenario. Read full transcript
The first gives us the things that we have to move around, a 0, 1, 2, 3 and 4. Those are the things we will be placing in those spaces 1 through 5. So don't confuse the digits that we're moving with the digits in the code. So essentially, there's a first digit, but there's also the digit 1 that could be in any one of those places. It could be second, third, or fourth and so on.
Now, the next rule is a loophole closer. It says that you have to use each digit only once. So since you have five digits, you have five slots. Now, the real rules start at rule three. The second digit has to be exactly twice the first. Now, numerically, there's only two ways that could work out.
You need two numbers, one of them twice the other. So that could either be 1 and 2 or 2 and 4. Now, when there's something that big in a game, it suggests that you might wanna draw it both ways. Split your sketch into two templates, one where you put 1 and 2 first, and one where you put 2 and 4 first.
And the fourth rule is that the value of the third digit has to be less than the value of the fifth. So think about it one at a time. In the top sketch, we've already used our 1 and 2, so we have 0, 3, and 4 left. In the bottom sketch, we've already used our 2 and 4, so we have a 0, 1, and 3 left.
Since the third digit has to be less than the fifth, in the top, it won't be allowed to be 4, and in the bottom it won't be allowed to be 3. Because we have to save a number that's larger than the third digit for the fifth digit. That's also going to limit the fifth digit. So if the fifth digit has to be bigger than the third digit.
In our top option there, it's not gonna be allowed to be 0. It's either gonna have to be 4 or 3. And in the bottom scenario, same deal. It's not gonna be allowed to be 0, it'll have to be either 1 or 3. And that's about as specific as we can get. But at this point, the sketch is pretty narrow.
There's not a whole lot left to move around, only the fourth digit is completely unconstrained. So let's go into the questions. Now, the best order to tackle the questions in is to do the local questions first, then move on to your global questions. So the best order here would be to go question one, then three, and then double-back, pick up two and go on to four and five.
So let's go on to the questions.