## Saturday, 25 January 2014

### 6 AM Quiz: Bridge Crossing

The 6 AM Quiz is a platform to engage those who would like to seek deeper exploration and understanding of selected topics. It is therefore not compulsory.

While you tried to solve the puzzle, what mathematical knowledge and skills did you apply to solve the problem?

1. I managed to solve the game with 29336 points. First I crossed with 1 and 3, then took 1 back. Then I crossed with 1 and 6 and took one back. Then I crossed 8 and 12 and took 3 back. Lastly, I crossed 1 and 3 and I won with I lamp life to spare

1. Chen Ning
Do you use some strategies to decide who to move first?

2. I figured that I needed to place a "fast" person on each side of the bridge so the lamps could be quickly brought over if needed to. Since the old woman and pink lady were the slowest, I crossed them together so less time would be wasted.

2. Solution: Let 1 and 3 be the "lamp carriers" that carry the lamp from left to right.
Move 1 and 3 to the left and move 3 back to the right, so 1 can bring back the lamp later. Once the lamp is back to the right, move 2 slow people to the left together, and let 1 bring the lamp back to the right. Keep doing this until all are to the left.

1. Xavien
In summary, what's the strategy you use - to help you decide who to move first? and who are the ones to be paired together?

3. First I will move the fastest and 2nd fastest across. The fastest will cross back to the other side. Then, the slowest and second slowlest will move across. The second fastest person will move back across to the other side. The first and third fastest will move across. Then, the fastest comes back for the second fastest person.He and the fastest person will move across. Since there is a limited time, and each person has a different speed, I let the slowest and second slowest person go together to save time.

1. Wai Yan
In the description, you have somehow mentioned the strategy - So, in summary, what's the strategy you apply to decide who to pair with and who to move first?

2. I moved the fastest and second fastest first since they walked faster than everyone and can be used to help other people later. I moved the 2 slowest people next to save time as if I moved them 1 by 1, it would be wasting time. Then, I chose the 2nd fastest person to move the lamp to the other side. Next I first let the fastest and third fastest person to cross and let the fastest come back for the second fastest person, again, for saving time.

4. I finished it and used the same method as Wai Yan
This game tests you on your common sense. You will have to move all the people in a way that the people will all be on the left side by the time limit. which is the method Wai Yan used. The most important thing is that the 2 slowest people must move through the bridge together so it saves a lot of time. But we must also ensure one of the faster people is on the other side. Or else, time would be wasted as the 2nd slowest will have to bing the lamp back which will take up 8 minutes So the first step is to just bring the 2 fastest people over and bring one back to bring the lamp for the two slowest people. After they cross the bridge, the faster one can bring the lamp back for the other people. Then the fastest person can bring the third fastest person over so the the fastest person can bring the lamp back the the right side in the shortest time possible. And then bring both the persons on the right over the bridge which will help you beat the game

5. The fastest two players are need to carry the lamp. I used the fastest two to bring the lamp over the other side, then using the fastest to bring it back. Next, I sent the two slowest ones over and used the second fastest one to bring back the lamp. Next, I used the fastest one to bring the slow one left to the other side. The fastest one then brought the lamp back and the two fastest ones went to the other side, with a minute to spare.

6. This comment has been removed by the author.

7. By testing out the game, I realised that the numbers representing the player was the amount of time they took to complete crossing the bridge once. So, I crossed the bridge with 1 and 3, since they can cross the bridge faster. Then I brought 1 back.. This time, I crossed with 1 and 6 and brought one back. I did this because if I crossed with 8 and 12 first, 3 had to cross the bridge instead of 1 and 2 minutes of lamp time will be wasted. Then, 8 and 12 crossed the bridge, because I figured that if they travelled together with 1 seperately, they would take a total of 22 minutes to cross the bridge, including the amount of time 1 had to take to cross back and the lamp time would have expired or expire soon. Lastly, I brought 3 back and brought 1 and 3 across, and completed the game with a minute of lamp time to spare. ( I deleted the previous comment as I had not yet completed my explanation.)

1. Also, this method is similar to Wai Yan's.

8. By playing the game, the thing I managed to realise is the number of the person is also the speed of the person. This game basically wants to know how fast you are and how much common sense you use to figure out how fast a person can walk to the other edge of the bridge. First, move the people with walking speeds of 1 and 3 minutes to the left and then I move the person with walking speed of 1 minute back to the right. Move the persons with walking speeds of 8 and 12 minutes to the left and move the person with walking speed of 3 minutes back to the right. Move the persons with walking speeds of 1 and 6 minutes to the left and move the person with walking speed of 1 minute to the right. Move the persons with walking speeds of 1 and 3 minutes to the left ending the game. Similar to Wai Yan's one most probably.

9. When returning, it is the two fastest walkers who must return. When crossing the bridge, the slower walkers should go together.(12 and 8)
1 and 3 go first and 3 returns. Then 12 and 8 go and 1 returns. Then 6 and 1 go and 1 returns.3 and 1 go.

10. I moved the faster two first and then move the fastest back.After that i moved the two slowest to the other side,then returned the second fastest back.I sent the fastest together with the third fastest then completed it by sending the fastest back to collect the second fastest and moving them together.PS I just reached home and i know its late