## Saturday, 19 January 2013

### 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. This comment has been removed by the author.

2. My score is 28830.
I used common sense to solve the problem. It looked familiar to me as i have already seen it.
This is the solution
1st: 1 and 3 go over.
2nd: 3 comes back.
3rd: 8 and 12 go over.
4th: 1 comes back.
5th: 1 and 6 go over.
6th: 1 comes back.
7th: 1 and 3 go over.

1. Can further describe the 'strategy', as on how you decide upon "1" and "3" shall go first, and why you 'send' "3" back? (etc)

2. i think what he meant was to use the fastest, 1 and 3 to transport ppl abt. since they are the fastest they save time

3. i sent the '3' back so as to let one bring back the lamp after the next two cross as he is fastest.

4. actually the other way around is also possible

3. Possible solution:

Move 1 and 3 across, move 1 back
Move 8 and 12 across, move 3 back
Move 1 and 6 across, move 1 back
Move 1 and 3 across, finished

When i tried to solve the puzzle, i re-tried it many times as i wanted to find a way to save time when the 2 slowest people crossed the bridge. I didn't really apply any mathematical skills honestly, just logical thinking.

1. One of the strategies/ considerations you have in mind is moving the "2 slowest people" to save time.
Does this apply throughout the entire "transportation" process?
What else did you consider when moving the rest?

2. she had to move the slowest people first, together with the fast ones, so they do not take alot of time to return, then they bring others across. this saves time wen moving back to bring others across

3. It kind of does apply, because I try and move 6, 8 and 12 across first, with 1 and 3 speeding up the 'going back and picking up another person' process. Like what I've just mentioned, I considered about the going back process as i want it to be as fast as possible to not waste the lamp time.

4. I considered moving both of them at once to save the time of moving one of them back but the actual strategy is to use 1 and 3 to move the lamp around as they are the fastest. As such, we must use both of these to help us in our answer. Thus, I moved the two fastest people first before moving the two slowest people so there was a fast person waiting to bring the lamp back.

5. The time for two people to cross in the game is the longer time of the two. So for example, if you move the 1 minute guy and the 12 minute guy together, they will still take 12 minutes to cross, which is a total waste of time!
Sorry not trying to insult the 老aunties out there :P

4. i also retried it many times

1. As you tried... how did you "sharpen" your strategy?
Ok... did you make your attempts 'systematically'?
:)

2. one has to try it with the next stargety he can think, or else, try again.

3. Its strategy, not stargety

5. my score is 12110.
i let the larger numbers cross one with the help of the smaller ones.
this is it:
1&3 go
3 comes back
3 8, 12 and 6 cross one at a time
3 returns

2. Collin has made an attempt to highlight his strategy, which can be further elaborated [Line 2]
:)

3. i also dk
i just use 1&3 to move ppl abt.

6. Looks like there are several ways to solve the problem...
Is there unlimited ways or there's a finite number of solution?

1. i think there are ways unknown but limited.
these can vary from logic to mathematics and even planning

2. There is a finite number of answers as there are a finite number of permutations in the question in the first place.

3. Let's see if we are able to see all the possible answers by the end of the day :)

4. it is hard to record these answers and there are a lot, although limited. it will be hard to find these answers as half of them can be from different plans. like a qn saying 18=2x3x3 the factors are therefore 1, 2, 3, 6, 9 and 18. in this qn we multiplied different numbers in different ways. same goes for this quiz

5. finite
was I very slow? and do we need to explain our answers?

7. solution :
1] move '1' and '3' to the left side of the bridge first
2] move '3' back to the right side of the bridge
3] move '8' and '12' to the left side of the bridge
4] move '1' back to the right side of the bridge
5] move '6' and '1' to the left side of the bridge
6] move '1' to the right side of the bridge
7] move '1' and '3' to the left side of the bridge

1. Share with us your 'strategy'... i.e. how you decide moving "1" and "3" first?

:)

2. tactic : try to get '12' and '8' across the bridge without having to move them back because that will waste alot of time

3. i moved '1' and '3' first because both of them are the fastest people and they take the least amount of time to cross the bridge so that '3' can come back and '1' can stay there to return after the slow poke '8' and '12' go across together [ which saves time ] :)

4. i feel what claire meant was to send the slowest over without them to come back. let the fastest cross the bridge

5. common strategy between all of us.

8. There is a finite number of answers as there are a finite number of permutations in the question in the first place.

1. Let's see if we are able to see all the possible answers by the end of the day :)

9. 31878. Tried a 4 times.

1. Did you apply the same strategy for all 4 times?

10. 1 and 3 go first. 1 come back. Then 1 and 6 will go together. 1 will come back again. 8 and 12 will cross the bridge. 3 comes back. Finally 3 and 1 will come back with a remainder of one minute.
I used logical thinking to solve the problem.The person with the shortest time(1) and the second shortest time(3) should go first and the person with the third shortest time(6) should go second after 1 returns back with the lamp. 1 will return back so that those who will take longer time(8) and(12) should go now because they two will finish in just 12 minutes instead of 8 and 12 separately(which make 20 min). 1 will be left over. The reason why 3 has crossed the bridge before is in case 1 did not cross the bridge. So 3 will go instead of 6 since it takes a shorter time since the lamp will only light up for 30 min. 1 and 3 comes back and they are done with it!

1. Detailed description :)
Next, let's see if you could 'summarise' the strategy employed in this entire transportation?

:)

2. 1) Move 1 and 3 to cross the bridge.
2) Move 1 back to the right side of the bridge.
3) Move 1 and 6 to cross the bridge.
4) Move 1 back to the the right side of the bridge.
5) Move 8 and 12 to cross the bridge.
6) Move 3 back to the right side of the bridge.
7) Finally move 1 and 3 to cross the bridge and it's done.

11. My score was 30511, with the lamp life remaining at 1 minute.
!st step: I moved the guy who takes 1 minute to cross the bridge to move across with the guy who takes 3 minutes.
2nd step I moved the guy who took 1 minute to cross the bridge back.
Reason: I did the first step because I wanted to move the fastest people across first so that I could save time. Then, to save time, I moved the guy who took one minute to cross the bridge back to where he was at the beginning of the game.
3rd step: I moved the old auntie who took 12 minutes and the lady who took 8 minutes to cross the bridge.
Reason: I did this step so that I could save time, moving the two slowest people together. Altogether, when the two slowest people moved together, they only took the longer time of 12 minutes when both the old auntie who took 12 minutes to cross the bridge and the lady who took 8 minutes crossed together. During my previous tries, I actually moved the guy who took 1 minute to cross the bridge along with the old auntie, who took 12 minutes to cross. In the end, I wasted time, moving the slowest people seperately.
4th step: I made the guy who took 6 minutes cross the bridge along with the guy who took 1 minute.
Reason: I wanted to do this because it would help to save time.(I will explain the rest in the later steps.)
5th step:I moved the guy who took 1 minute to cross the bridge back to the starting point.
Reason: In the forth step, I decided not to move the guy who takes 3 minutes to cross the bridge with the guy who took 6 minutes to cross as when he was going back to the starting point, he would take 3 minutes as compared to the guy who takes 1 minute to cross(this guy will also take 1 minute to walk back to the starting point.) The reason for the forth step is so that I could move the guy who takes 3 minutes to cross back with him.
5th step: I moved the guy who took 1 minute to cross and the guy who took 3 minutes to cross back together.
Reason: To complete the game!

1. Clear description of the thinking... and interestingly, you have brought in your "review" of the previous attempts :)
Now, how would you summarise the strategy?

:)

2. Ms loh, what do you mean by summarise? :D

3. Sorry the last step should be the 6th step.

12. Having seen a number of "possible solutions"... is there one "most efficient" way to solve this problem? #iwonder :)

1. I tried it about six times,mixing it here and there , but at the end,there is always 1 min of lamp life left