Challenge Questions Blog

Challenge Questions

Stop in and exercise your brain. Talk about this month's Challenge from Specs & Techs or similar puzzles.

So do you have a Challenge Question that could stump the community? Then submit the question with the "correct" answer and we'll post it. If it's really good, we may even roll it up to Specs & Techs. You'll be famous!

Answers to Challenge Questions appear by the last Tuesday of the month.
Previous in Blog: Spark Safety: Newsletter Challenge (November 2013)   Next in Blog: Brass Plate Heating: Newsletter Challenge (January 2014)
Close

Comments Format:






Change Mode
Close

Subscribe to Discussion:

CR4 allows you to "subscribe" to a discussion
so that you can be notified of new comments to
the discussion via email.

Close

Rating Vote:







Add Vote
15 comments
Rating: Comments: Nested

Expansive Expansion: Newsletter Challenge (December 2013)

Posted December 01, 2013 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from GlobalSpec:

A binomial raised to the 3rd power and then algebraically expanded has binomial coefficients of 1, 3, 3, 1. What are the binomial coefficients when a binomial is raised to the 16th power?



And the answer is:

Pascal's Triangle makes this an easy problem to solve. Simply use the bottom row below to obtain the coefficients for each term. For trinomial expansions there is a similar tool called Pascal's pyramid.

Reply

Interested in this topic? By joining CR4 you can "subscribe" to
this discussion and receive notification when new comments are added.

Comments rated to be Good Answers:

These comments received enough positive ratings to make them "good answers".
2
Doorman
Guru
Hobbies - DIY Welding - Don't Know What Made The Old Title Attractive... Popular Science - Weaponology - New Member United States - US - Statue of Liberty - 60 Year Member

Join Date: Apr 2009
Location: Yellowstone Valley, in Big Sky Country
Posts: 6960
Good Answers: 283
#1

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/01/2013 1:02 AM

1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1

Never memorize something that you can look up.
Albert Einstein

__________________
 When you come to a fork in the road, take it. (Yogiism)
Reply Good Answer (Score 2)
Go to Next Good Answer
2
Tornado
Guru
Technical Fields - Technical Writing - New Member Engineering Fields - Piping Design Engineering - New Member

Join Date: May 2009
Location: Richland, WA, USA
Posts: 20986
Good Answers: 781
#2

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/01/2013 3:56 AM

If you don't want to look it up, just do a Pascal's Triangle.

__________________
 In vino veritas; in cervisia carmen; in aqua E. coli.
Reply Good Answer (Score 2)
Go to Next Good Answer
Doorman
Guru
Hobbies - DIY Welding - Don't Know What Made The Old Title Attractive... Popular Science - Weaponology - New Member United States - US - Statue of Liberty - 60 Year Member

Join Date: Apr 2009
Location: Yellowstone Valley, in Big Sky Country
Posts: 6960
Good Answers: 283
#3
In reply to #2

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/01/2013 1:18 PM

Yup.

__________________
 When you come to a fork in the road, take it. (Yogiism)
Reply
RufusVS
Guru

Join Date: Dec 2010
Posts: 511
Good Answers: 46
#9
In reply to #2

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/02/2013 2:05 PM

Ditto.
Reply
2
Usbport
Guru
Engineering Fields - Optical Engineering - Member Engineering Fields - Engineering Physics - Member Engineering Fields - Systems Engineering - Member

Join Date: Apr 2010
Location: Trantor
Posts: 5363
Good Answers: 646
#4

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/01/2013 2:54 PM

Since the general form is (ax + by)n, the coefficients of the expanded general form of the binomial to the 16th power would be:

1a16, 16a15b, 120a14b2 560a13b3, 1820a12b4, 4368a11b5, 8008a10b6, 11440a9b7, 12870a8b8, 11440a7b9, 8008a6b10, 4368a5b11, 1820a4b12, 560a3b13, 120a2b14, 16ab15, 1b16

/Another exciting challenge.

__________________
 Whiskey, women -- and astrophysics. Because sometimes a problem can't be solved with just whiskey and women.
Reply Good Answer (Score 2)
Go to Next Good Answer
Doorman
Guru
Hobbies - DIY Welding - Don't Know What Made The Old Title Attractive... Popular Science - Weaponology - New Member United States - US - Statue of Liberty - 60 Year Member

Join Date: Apr 2009
Location: Yellowstone Valley, in Big Sky Country
Posts: 6960
Good Answers: 283
#5
In reply to #4

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/01/2013 3:28 PM

Yup.

__________________
 When you come to a fork in the road, take it. (Yogiism)
Reply
Tornado
Guru
Technical Fields - Technical Writing - New Member Engineering Fields - Piping Design Engineering - New Member

Join Date: May 2009
Location: Richland, WA, USA
Posts: 20986
Good Answers: 781
#6

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/02/2013 4:21 AM

This time they can publish the answer on the first, rather than last, Tuesday of the month.

__________________
 In vino veritas; in cervisia carmen; in aqua E. coli.
Reply
Usbport
Guru
Engineering Fields - Optical Engineering - Member Engineering Fields - Engineering Physics - Member Engineering Fields - Systems Engineering - Member

Join Date: Apr 2010
Location: Trantor
Posts: 5363
Good Answers: 646
#7
In reply to #6

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/02/2013 9:58 AM

As doorman would say: yup.

__________________
 Whiskey, women -- and astrophysics. Because sometimes a problem can't be solved with just whiskey and women.
Reply
Doorman
Guru
Hobbies - DIY Welding - Don't Know What Made The Old Title Attractive... Popular Science - Weaponology - New Member United States - US - Statue of Liberty - 60 Year Member

Join Date: Apr 2009
Location: Yellowstone Valley, in Big Sky Country
Posts: 6960
Good Answers: 283
#8
In reply to #6

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/02/2013 12:14 PM

Yup.

I remember this being ladled out in high school physics or trig. Is this still the case?

__________________
 When you come to a fork in the road, take it. (Yogiism)
Reply
SolarEagle
Guru

Join Date: Mar 2007
Location: at the beach in Florida
Posts: 31327
Good Answers: 1736
#10

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/03/2013 12:46 AM

__________________
 Break a sweat everyday doing something you enjoy
Reply
RufusVS
Guru

Join Date: Dec 2010
Posts: 511
Good Answers: 46
#11
In reply to #10

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/03/2013 11:07 AM

In case you didn't guess, what SolarEagle showed you here was the aforementioned "Pascal's Triangle" (or at least the top 17 rows...)
Reply
2
trosenberger
Active Contributor

Join Date: Apr 2013
Posts: 15
Good Answers: 2
#12

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/03/2013 2:17 PM

Generally, any coefficient is n!/(m!*(n-m)!) where n is the binomial exponent and m is the ordinate of the coefficients of the expansion working from left to right (or right to left - gotta love symmetry)
Reply Good Answer (Score 2)
No more Good Answers.
James Stewart
Guru
Safety - Hazmat - New Member United States - US - Statue of Liberty - New Member Engineering Fields - Chemical Engineering - Old Hand

Join Date: Mar 2011
Location: Lubbock, Texas
Posts: 14331
Good Answers: 161
#13
In reply to #12

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/03/2013 5:46 PM

That is why I leave the higher algebra to those who are complete whizzed (Ghengi even) at algebra. I hate to admit the answer did not automatically roll off the tip of my tongue, and as usual, am the last dog to the bowl anyway.

__________________
 If it ain't broke, don't fix it. Just build a better one.
Reply
prof peanut
Power-User

Join Date: Dec 2013
Posts: 199
Good Answers: 5
#14

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/03/2013 6:06 PM

1,16,120,560,1820,4368,8008,11440,12870,11440,8008,4368,8008,4368,1820,560,

120,16,1. I am glad to see that my notes on Pascals triangle from 25 years ago are correct.
Reply
WilhelmHKoen
Guru

Join Date: Mar 2009
Posts: 507
#15

Re: Expansive Expansion: Newsletter Challenge (December 2013)

12/04/2013 12:21 AM

the binominal coeffizients ar3:

1 16 120 560 1820 4368 8008 11440 12870 12870 11440 8008 4368 1820 560 120 16 1

or take a pohl
Reply
Reply to Blog Entry 15 comments
Interested in this topic? By joining CR4 you can "subscribe" to
this discussion and receive notification when new comments are added.

Comments rated to be Good Answers:

These comments received enough positive ratings to make them "good answers".
Copy to Clipboard

Users who posted comments:

Doorman (4); James Stewart (1); prof peanut (1); RufusVS (2); SolarEagle (1); Tornado (2); trosenberger (1); Usbport (2); WilhelmHKoen (1)

Previous in Blog: Spark Safety: Newsletter Challenge (November 2013)   Next in Blog: Brass Plate Heating: Newsletter Challenge (January 2014)

Advertisement

Got Something to Say?
Ask a Question
Start a Discussion

Search this Section
General:
Go

Search this Blog
Challenge Questions:
Go

Recent Blog Entries

CR4 Sections
Aerospace
BioMech & BioMed
Chemical & Material Science
Civil Engineering
Communications & Electronics
Education and Engineering Careers
Electrical Engineering
General
Instrumentation
Manufacturing
Mechanical Engineering
New Technologies & Research
Software & Programming
Sustainable Engineering
Transportation

Site Directories
Forum Directory
Blog Directory
User Group Directory
RSS Feeds

CR4 Rules of Conduct
CR4 FAQ
Site Glossary

Who's Online (37 right now)
Show Members
Advertisement