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# You have a 3 sided triangular based pyramid with 3 cans of paint

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Intern
Joined: 18 May 2016
Posts: 34
You have a 3 sided triangular based pyramid with 3 cans of paint  [#permalink]

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27 Sep 2018, 14:41
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

16% (01:57) correct 84% (01:44) wrong based on 63 sessions

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You have a 3 sided triangular pyramid and 4 cans of paint, each a different color. How many distinct ways can you paint the pyramid using a different color for each side? (If you can reorient the pyramid to look like another pyramid then the two pyramid are not distinct.)

(A) 2
(B) 4
(C) 6
(D) 8
(E) 20
Math Expert
Joined: 02 Aug 2009
Posts: 8005
Re: You have a 3 sided triangular based pyramid with 3 cans of paint  [#permalink]

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27 Sep 2018, 19:56
2
1
plalud wrote:
You have a 3 sided triangular pyramid and 4 cans of paint, each a different color. How many distinct ways can you paint the pyramid using a different color for each side? (If you can reorient the pyramid to look like another pyramid then the two pyramid are not distinct.)

(A) 2
(B) 4
(C) 6
(D) 8
(E) 20

3-sided triangular pyramid means all FOUR faces are triangles....
so we can make the base as one of vertical faces and vice versa..
so the way you colour 3 vertical faces will encompass all other when each face is converted as base one by one..

so we have to see how we can colour the 3 vertical faces..
now 3 vertical faces is nothing but a circular arrangement so ways (3-1)! = 2!=2 ways

A
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Joined: 23 Jun 2015
Posts: 26
Re: You have a 3 sided triangular based pyramid with 3 cans of paint  [#permalink]

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28 Sep 2018, 23:19
chetan2u wrote:
plalud wrote:
You have a 3 sided triangular pyramid and 4 cans of paint, each a different color. How many distinct ways can you paint the pyramid using a different color for each side? (If you can reorient the pyramid to look like another pyramid then the two pyramid are not distinct.)

(A) 2
(B) 4
(C) 6
(D) 8
(E) 20

3-sided triangular pyramid means all FOUR faces are triangles....
so we can make the base as one of vertical faces and vice versa..
so the way you colour 3 vertical faces will encompass all other when each face is converted as base one by one..

so we have to see how we can colour the 3 vertical faces..
now 3 vertical faces is nothing but a circular arrangement so ways (3-1)! = 2!=2 ways

A

Hii Chetan ..
It is clear for circular arrangement . But there are 4 different colors available . But why you are selecting colors only from 3 colors ??
If you say one color is applied to base , even in that case we have to select that color from 4 different paints available right ??
Please explain me in detail . I am confused with this question
Manager
Joined: 21 Jun 2017
Posts: 232
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: You have a 3 sided triangular based pyramid with 3 cans of paint  [#permalink]

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13 Oct 2018, 09:58
karnaidu wrote:
chetan2u wrote:
plalud wrote:
You have a 3 sided triangular pyramid and 4 cans of paint, each a different color. How many distinct ways can you paint the pyramid using a different color for each side? (If you can reorient the pyramid to look like another pyramid then the two pyramid are not distinct.)

(A) 2
(B) 4
(C) 6
(D) 8
(E) 20

3-sided triangular pyramid means all FOUR faces are triangles....
so we can make the base as one of vertical faces and vice versa..
so the way you colour 3 vertical faces will encompass all other when each face is converted as base one by one..

so we have to see how we can colour the 3 vertical faces..
now 3 vertical faces is nothing but a circular arrangement so ways (3-1)! = 2!=2 ways

A

Hii Chetan ..
It is clear for circular arrangement . But there are 4 different colors available . But why you are selecting colors only from 3 colors ??
If you say one color is applied to base , even in that case we have to select that color from 4 different paints available right ??
Please explain me in detail . I am confused with this question

Suppose your base 1 is red. Then other 3 faces are Green Blue and Yellow. If you keep this in your palm with red side on it, you can rotate this pyramid in 2 ways. Clockwise and anti clockwise.
Now lets change the base. Let the base be green and other faces be red yelloe blue. Now again when you try to rotate , the same figure is generated. So the total no of orientations is just two. Also keep in mind, we have only 4 paints and 4 faces to paint. Had there been more paints and lesser facs faces, situation would have been different.

Hope this makes sense.
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Re: You have a 3 sided triangular based pyramid with 3 cans of paint   [#permalink] 13 Oct 2018, 09:58
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