The Pup Tent Problem

***Ace Mercury*** · 06-13-2009, 10:06 PM

Here's one that I didn't get right the first time, and still kinda can't visualize. (And I thought I was good at 3D stuff.)

The Pup Tent Problem | Futility Closet

Quote:

In 1980 the Educational Testing Service offered this question on an aptitude test:

In pyramids ABCD and EFGHI shown above, all faces except base FGHI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?

(A) Five (B) Six (C) Seven (D) Eight (E) Nine

Which is correct?

Microphone_Kirby · 06-13-2009, 10:43 PM

(C) Seven

***Saria Dragon of the Rain Wilds*** · 06-13-2009, 11:48 PM

Spoiler Below

5, due to the tilting required to make the faces touch

**Deku Trii** · 06-13-2009, 11:56 PM

Spoiler Below

I believe it's 5. I think two faces of ABCD run flush with two faces of EFGHI in a way that sort of merges those faces, but the third face of ABCD doesn't run flush with the base of EFGHI.

**Cravdraa** · 06-14-2009, 12:34 AM

Spoiler Below

Five. Six if you count the bottom of FGHI.

Blake · 06-14-2009, 04:39 AM

Spoiler Below

I don't quite understand the question so I'd say six or eight.

I am nobody · 06-14-2009, 06:56 AM

Spoiler Below

7, assuming you count the bottom faces as exposed.

EDIT: And suddenly I remember why I don't like pyramids. >_<

***Ace Mercury*** · 06-23-2009, 08:47 AM

Well, for those who didn't click through to the link, the answer is here: “The Pup Tent Problem”: Solution | Futility Closet

Personally, I enjoy problems where I get it wrong, and then I can figure out why I got it wrong.

06-13-2009, 10:43 PM	#2
Microphone_Kirby Senior Member Join Date: Apr 2003 Location: None of your business. Gender: Posts: 7,013 Thanks: 525 Thanked 223 Times in 179 Posts Blog Entries: 6	(C) Seven

06-13-2009, 11:48 PM	#3
*Saria Dragon of the Rain Wilds* Admin "mine.. not yours. NO. MINE." Epic Ladynerd Join Date: Jul 2000 Location: Forteresse de Valois Gender: Posts: 28,199 Thanks: 1,510 Thanked 1,719 Times in 993 Posts	Spoiler Below 5, due to the tilting required to make the faces touch

06-13-2009, 11:56 PM	#4
Deku Trii PP&R Mod Current Events Mod Join Date: Jun 2000 Location: Texas Gender: Posts: 8,930 Thanks: 490 Thanked 1,063 Times in 559 Posts	Spoiler Below I believe it's 5. I think two faces of ABCD run flush with two faces of EFGHI in a way that sort of merges those faces, but the third face of ABCD doesn't run flush with the base of EFGHI.

06-14-2009, 12:34 AM	#5
Cravdraa VGF RPG Mod Join Date: May 2001 Location: It's Round on the sides and high in the middle. Gender: Posts: 8,099 Thanks: 156 Thanked 593 Times in 368 Posts	Spoiler Below Five. Six if you count the bottom of FGHI.

06-14-2009, 04:39 AM	#6
Blake Senior Member Join Date: Sep 2001 Location: A generic place such as a house Gender: Posts: 4,564 Thanks: 1,425 Thanked 204 Times in 146 Posts	Spoiler Below I don't quite understand the question so I'd say six or eight.

06-14-2009, 06:56 AM	#7
I am nobody Senior Member Join Date: Aug 2007 Location: Over there. Gender: Posts: 5,515 Thanks: 309 Thanked 365 Times in 242 Posts Blog Entries: 7	Spoiler Below 7, assuming you count the bottom faces as exposed. EDIT: And suddenly I remember why I don't like pyramids. >_<

06-23-2009, 08:47 AM	#8
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 22,962 Thanks: 558 Thanked 3,205 Times in 1,531 Posts Blog Entries: 1	Well, for those who didn't click through to the link, the answer is here: “The Pup Tent Problem”: Solution \| Futility Closet Personally, I enjoy problems where I get it wrong, and then I can figure out why I got it wrong.