Path counting brain teaser (video) | Puzzles | Khan Academy
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Please help by adding reliable sources. Assuming driver 1 is in compliance at 1: This was accomplished by getting two periods of rest, one being 8 hours in the sleeper and the other being 2 hours in the sleeper. This calculation will be discussed in greater detail below. Driver 2, assumed to be in compliance at 9: Driver 2 enters the sleeper berth at After exiting the sleeper at 7: How do we determine how many hours each driver has available after finishing a break?
Keep these basic rules in mind: After the second of two required rest periods, calculate available time by starting at the end of the first period. In other words, once you have two qualifying breaks that add up to 10, the time you used before the first break and the first break itself drops out of consideration. You can exclude from your hour calculation any sleeper-berth period of 8 or more consecutive hours, but you must include all other sleeper or off-duty periods.
This means one of the two required rest breaks will likely count against you, unless you always get 8 hours or more in the sleeper. We can now ignore the time spent before the first break 1: After driving another 8 hours, the driver enters the sleeper for another 8 hours, until 3: We start counting at So the driver has 3 hours of driving time available within a 6-hour window. Calculations for driver 2 are handled the same way. Note, however, that the 8-hour sleeper period on Day 1 does NOT count as one of the two required rest breaks for this driver, because it is part of a larger hour off-duty period.
I Need a Break! The sample logs provided above present a theoretical situation where the drivers are able to maximize their driving time. In the real world, drivers are not machines, and most will not be able to drive for 8 hours without stopping for food, fuel, bathroom breaks, etc.
Drivers, motor carriers, and dispatchers will have to work together to develop a route plan that works for their particular needs while allowing time for personal and vehicular necessities.
For example, a driver facing 8 solid hours of driving may be able to stop every few hours while the co-driver stays in the sleeper berth, or both drivers may be able to enter a truck stop at the same time before trading places. Extending the Day Note that an 8-hour sleeper period is always excluded from the hour calculation, even if it is not combined with a later or previous 2-hour break.
After 10 hours off, a driver could, for example, drive for 6 hours, sleep in a sleeper berth for 8 hours, and then drive another 5 hours. If a driver spends more than 2 hours in the passenger seat of a moving vehicle, the time beyond 2 hours must be logged as "on duty" time and will count against the hour limit.
Passenger-Carrying CMVs The driver of a passenger-carrying commercial motor vehicle cannot drive for more than 10 hours following 8 consecutive hours off duty. One way to go there.
Similarly, you can kind of view these as symmetric. I mean, when you go straight to the right, this is if you go straight down. So this is one way. Just straight all the way down.
Now let's do a slightly more interesting cell. How many ways are there to get to this cell right here? Well, this first time, let's draw it out. We could either go down and to the right.
And we could go right and down. Right, so there's two ways to get to this cell. And this was easy to do to work out all the ways, because there aren't that many. But you might already see an interesting pattern.
If I have a cell here. Let me draw a couple of cells. Let me draw it like that. And draw it like that. And let's just say this is some arbitrary cell someplace in this grid. It doesn't even have to be a six by six grid. It can be an n by n grid. We could do this problem with by But then the video would take long to do all of the math.
But let's say I want to figure out how many ways can I get to this cell right here? And let's say I know that there are n ways to get to this cell. And m ways-- not n --m ways to get to that cell. So how many ways can I get there? Well the only way to get to this cell-- and I'll do it in another color --the only way to get to this cell, based on the rules I gave you, is either to go straight down or go straight to the right. So you can either go from this cell, straight down.
Or you can go from this cell and straight to the right. So how many total ways can you get to this cell?
Well the only ways you could have gotten to this cell is by going down from here. But there was n ways you could have gotten there.
So there's n total ways that you could get to this cell, and then go to this cell. And then there's m ways that you could get to this cell, and then go to this cell. So this cell-- or this box --I keep using the word cell, maybe because my brain is fixated on Excel.
There are n plus m ways to get to it. And hopefully you understand that intuition. Because there's two ways to get to this cell directly, from that one and from that one. And I'm saying that there's n ways to get there. So of all of the ways to get here, there's n ways to get here before that. And same logic for that. And you saw that right here. With the two, is one plus one. So there's two ways to get there. And let's see if that logic holds one more time. Just because, I don't want you to just take this as a leap of faith.
It should make sense to you. So how many ways are there to get here?
Path counting brain teaser
So based on what I just told you, I should just be able to add two plus one, and say three. But let's see if that works out. So I could go all the way to the right. I could go two. Then I could go down and that way. And notice, out of all of the three ways to get here, one of them comes from this cell.
count | Definition of count in English by Oxford Dictionaries
And two of them comes from this cell. So that makes sense, relative to the intuition I just gave you. So let's just fill out this box. Let's just fill out the box.