Problem number 23. Kengi's car can only turn left. It can never turn right. Which of the following five routes can Kengi take to get from one black dot to the other? A, B, C, D, or E? Kengi can start on either dot on the route. So all we need to find is a path where the turns are all in the same direction. If we find one that has all right turns, then if Kengi went the reverse way from the other dot to the first dot, then it would be all left turns. Now let's look at each of the five routes. In solving this problem, it might get a little confusing as to whether we're turning left or right because sometimes the path is upside down. So we can think of these as clockwise or counterclockwise turns. The clockwise turns being to the right and the counterclockwise being to the left. Again, we just need to find a path where all the turns go the same direction. In A, if we start on this dot, here's our turn, left or counterclockwise. Another turn to the left, counterclockwise. Another one, counterclockwise. It is a left turn, even though the path now was coming from the top to bottom. The next turn is the same direction. Same, same, same, left or counterclockwise. So we have found the route. It's A. If Kengi starts on this dot, Kengi can get to the other dot by just making left turns. Just to make sure, let's briefly look at the other routes. In B, if we start here, the first turn is clockwise. That continues going clockwise, clockwise. But this turn is counterclockwise, as is this one. So we see that B does not have all the turns going the same. In C, if we start at this dot, we go clockwise, clockwise. Then, counterclockwise. So that's also not a path that would work. In D, if we start here, we'll go right or clockwise, clockwise, clockwise, clockwise, clockwise. You can see this very easily. It's pretty much a spiral. Clockwise, clockwise, clockwise. But then we get here, and it goes counterclockwise. So there will be turns in both directions. This is not a route that Kengi can take. In the card, it only turns left. And finally, E. Start at this dot. Go counterclockwise or left. Counterclockwise, counterclockwise, and clockwise. So with this clockwise turn, the turns are not all in the same direction. So this path does not work. So again, our answer is A. Kengi can start at this dot, take all left turns, and get to the second dot.

Kengi

left turns

route A

counterclockwise

navigation