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An ant is clinging to one corner of a box in the shape of a [#permalink]

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28 Jun 2012, 17:58

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An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?

An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?

A. 6 B.12 C.18 D.24 E.30

Make the cube and select two opposite corners. One where the ant is right now and the second is where it wants to reach. Notice that from its current position, it has 3 different paths that it can take i.e. it has 3 possible options. Make the ant move on any one path out of these 3. Once one path is chosen, it has two different paths it can take (it cannot take the third one since it cannot revisit the third point). Make the ant move on any one path out of these 2. Now, from this point, it again has 3 options to reach the point where it wanted to reach. Notice that the case will be the same even if you had selected different paths in the first two moves because it is a cube so all sides are the same.

Total number of different paths = 3*2*3 = 18
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Re: An ant is clinging to one corner of a box in the shape of a [#permalink]

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29 May 2014, 12:13

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@ Bunuel I have to type it all over again coz u deleted my last post..

Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible)

Either I misunderstood the Q and the E or the explanation is incorrect

I guess the way would be: No of ways to do in- 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways

Experts please comment
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Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..

An ant is clinging to one corner of a box in the shape of a [#permalink]

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12 Jul 2014, 20:07

VeritasPrepKarishma wrote:

vibhav wrote:

An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?

A. 6 B.12 C.18 D.24 E.30

Make the cube and select two opposite corners. One where the ant is right now and the second is where it wants to reach. Notice that from its current position, it has 3 different paths that it can take i.e. it has 3 possible options. Make the ant move on any one path out of these 3. Once one path is chosen, it has two different paths it can take (it cannot take the third one since it cannot revisit the third point). Make the ant move on any one path out of these 2. Now, from this point, it again has 3 options to reach the point where it wanted to reach. Notice that the case will be the same even if you had selected different paths in the first two moves because it is a cube so all sides are the same.

Total number of different paths = 3*2*3 = 18

Hi Karishma I could not get how there are three paths from the second point. Could you please explain in detail. Thanks

Re: An ant is clinging to one corner of a box in the shape of a [#permalink]

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16 Jul 2014, 11:55

JusTLucK04 wrote:

@ Bunuel I have to type it all over again coz u deleted my last post..

Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible)

Either I misunderstood the Q and the E or the explanation is incorrect

I guess the way would be: No of ways to do in- 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways

Experts please comment

Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted
_________________

Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..

@ Bunuel I have to type it all over again coz u deleted my last post..

Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible)

Either I misunderstood the Q and the E or the explanation is incorrect

I guess the way would be: No of ways to do in- 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways

Experts please comment

Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted

Here is the reason the number of paths is 3*2*3 and how it takes everything into consideration:

Attachment:

Ques3.jpg [ 6.31 KiB | Viewed 6151 times ]

I think the first two steps are clear so the first step is taken in 3 ways and second step in 2 ways. Now, draw the cube and see that the ant would be at one of three points (the points where you reach after traversing 2 edges) - E, C, G

For each of these points, there are 3 unique ways in which the ant can reach the desired vertex.

1st way - Directly go to the desired point. If it is an E, this means EF 2nd way - Go via 3 edges e.g. if it came from AD- DE, it goes EH-HG-GF 3rd way - Go via 5 edges e.g. if it came from AD- DE, it goes EH-HG-GB-BC-CF Since it is a cube, we know that what works for one edge, will work for other two as well.

So you multiply 3*2 by 3 to get 18.
_________________

@ Bunuel I have to type it all over again coz u deleted my last post..

Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible)

Either I misunderstood the Q and the E or the explanation is incorrect

I guess the way would be: No of ways to do in- 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways

Experts please comment

Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted

As for your solution, it is correct too, of course. You chose to split it into "number of paths used". But note the 1s you used in 5 steps and 7 steps. It means that paths are unique and the method involves some unnecessary counting. A cube gives us symmetry and it would be good to use that.
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Re: An ant is clinging to one corner of a box in the shape of a [#permalink]

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06 Sep 2015, 01:37

At first stage ant has three ways, right? At the second stage ant has only two ways, since it cannot return back on its path. At the third stage Ant has only one way to its destination. Henceforth, 3x2x1=6

Since there are three paths at the first stage we just need to add the outcomes of each three ways: 6+6+6=18

An ant is clinging to one corner of a box in the shape of a [#permalink]

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29 Oct 2016, 00:24

VeritasPrepKarishma wrote:

JusTLucK04 wrote:

JusTLucK04 wrote:

Bunuel I have to type it all over again coz u deleted my last post..

Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible)

Either I misunderstood the Q and the E or the explanation is incorrect

I guess the way would be: No of ways to do in- 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways

Experts please comment

Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted

Here is the reason the number of paths is 3*2*3 and how it takes everything into consideration:

Attachment:

Ques3.jpg

I think the first two steps are clear so the first step is taken in 3 ways and second step in 2 ways. Now, draw the cube and see that the ant would be at one of three points (the points where you reach after traversing 2 edges) - E, C, G

For each of these points, there are 3 unique ways in which the ant can reach the desired vertex.

1st way - Directly go to the desired point. If it is an E, this means EF 2nd way - Go via 3 edges e.g. if it came from AD- DE, it goes EH-HG-GF 3rd way - Go via 5 edges e.g. if it came from AD- DE, it goes EH-HG-GB-BC-CF Since it is a cube, we know that what works for one edge, will work for other two as well.

So you multiply 3*2 by 3 to get 18.

VeritasPrepKarishma ma'am I still didn't understand the 3rd multiple of 3. Could you please explain it again? Considering the ant starts from E and its destination being B, From point E it has 3 distinct path. When it gets to point D,H or F it has 2 distinct path through which it can reach B. Now comes the third point. From D it can come to A or C, From H it can go to A or G and from F it can go to C or G again giving rise to 2 distinct path. Ma'am could you please explain from here?

VeritasPrepKarishma ma'am I still didn't understand the 3rd multiple of 3. Could you please explain it again? Considering the ant starts from E and its destination being B, From point E it has 3 distinct path. When it gets to point D,H or F it has 2 distinct path through which it can reach B. Now comes the third point. From D it can come to A or C, From H it can go to A or G and from F it can go to C or G again giving rise to 2 distinct path. Ma'am could you please explain from here?

Re: An ant is clinging to one corner of a box in the shape of a [#permalink]

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01 Nov 2017, 21:38

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Re: An ant is clinging to one corner of a box in the shape of a [#permalink]

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02 Nov 2017, 09:12

This question has a bit of IQ test feel to it. You need to be able to visualize the paths to fit the problem to a standard permutations/combinations calculation.