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### Author Topic: Ponder This  (Read 3591 times)

#### app103

• That scary taskbar girl
• Global Moderator
• Joined in 2006
• Posts: 5,763
##### Ponder This
« on: October 09, 2007, 07:42 PM »
You are cordially invited to match wits with some of the best minds in IBM Research.

Seems some of us can't see a problem without wanting to take a crack at solving it. Does that sound like you? Good. Forge ahead and ponder this month's problem. We'll post a new one every month, and allow two to three weeks for you to submit solutions (we may even publish submitted answers, especially if they're correct). We won't reply individually to submitted solutions but every few days we will update a list of people who answered correctly. Towards the end of the month, we'll post the answer.

October 2007 Challenge:
There are 5 platonic solids, the tetrahedron (4 vertices, 4 triangular faces, 6 edges), the cube (8 vertices, 6 square faces, 12 edges), the octahedron (6 vertices, 8 triangular faces, 12 edges), the dodecahedron (20 vertices, 12 pentagonal faces, 30 edges) and the icosahedron (12 vertices, 20 triangular faces, 30 edges). Consider open models of these solids with wire edges connecting the vertices. Suppose each wire has unit resistance. For each case find the total resistance between a pair of adjacent vertices. Express each answer as a rational number.

Hint: The answers can be found by brute force but there is a way to use symmetry.

I can't even begin to understand the problems, nevermind solve them.

#### Darwin

• Charter Member
• Joined in 2005
• Posts: 6,984
##### Re: Ponder This
« Reply #1 on: October 09, 2007, 07:47 PM »
Is this even a development problem? Looks more like a straight forward puzzle to me. The answer is B, by the way. When in doubt, always answer B...

#### Ralf Maximus

• Supporting Member
• Joined in 2007
• Posts: 927
##### Re: Ponder This
« Reply #2 on: October 09, 2007, 08:50 PM »
The correct answer is, "some people have entirely too much time on their hands."

:-)

#### Lashiec

• Member
• Joined in 2006
• Posts: 2,374
##### Re: Ponder This
« Reply #3 on: October 10, 2007, 06:34 PM »
The legend says that engineers at Google are much worse...

#### Deozaan

• Charter Member
• Joined in 2006
• Points: 1
• Posts: 8,597
##### Re: Ponder This
« Reply #4 on: October 10, 2007, 09:44 PM »
Is this even a development problem? Looks more like a straight forward puzzle to me. The answer is B, by the way. When in doubt, always answer B...
-Darwin

I always pick "A" cause I have some Canadian friends.