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: Bears and Ferries, Oh My! (July '23 Challenge Question)   Next in Blog: A Deck of Cards in the Dark (September '23 Challenge Question)
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
6 comments
Rate this Comments: Nested

Counting to 1,000 by 3's (August 2023 Challenge Question)

Posted July 31, 2023 12:00 AM
Pathfinder Tags: challenge question

Bored? Need to stay busy?

How many different integers between the numbers 1 to 1,000 contain the digit 3 at least once? (i.e., the number 333 only counts once)

How many different instances of the digit 3 occur? (i.e, the number 333 counts thrice)

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".
3
SolarEagle
Guru

Join Date: Mar 2007
Location: by the beach in Florida
Posts: 33280
Good Answers: 1810
#1

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

07/31/2023 1:48 AM

271 numbers contain at least one three, and a total of 300 3's are used in total...

__________________
 All living things seek to control their own destiny....this is the purpose of life
Reply Good Answer (Score 3)
Go to Next Good Answer
Randall
Guru

Join Date: Aug 2005
Location: Hemel Hempstead, UK
Posts: 5803
Good Answers: 315
#2
In reply to #1

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

07/31/2023 8:05 AM

GA

Easy bit of "spreadsheeting"

__________________
 We are alone in the universe, or, we are not. Either way it's incredible... Adapted from R. Buckminster Fuller/Arthur C. Clarke
Reply
Rixter
Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9742
Good Answers: 1119
#3

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

07/31/2023 8:46 AM

1/10 have 3 in ones digit, 1/10 have 3 in tens digit, and 1/10 have 3 in hundreds digit, so 100 + 100 + 100 = 300 threes in all. (i.e., counting 333 as 3 instances).

Multiple threes:

Three threes: 1,: 333, subtract 1 x 2

Two threes: 3,: 330, 303, 033, subtract 3 x 1

300 - 1x2 - 3x1 = 295 numbers with one or more 3's
Reply
2
Rixter
Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9742
Good Answers: 1119
#4
In reply to #3

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

07/31/2023 9:03 AM

Correction:

1/10 have 3 in ones digit, 1/10 have 3 in tens digit, and 1/10 have 3 in hundreds digit, so 100 + 100 + 100 = 300 threes in all. (i.e., counting 333 as 3 instances).

Multiple threes:

Three threes: 1,: 333, subtract 1 x 2

Two threes: 3,: 33(9 digits), 3(9 digits)3, (9 digits)33, subtract 27 x 1

300 - 1x2 - 3x9 = 271 numbers with one or more 3's
Reply Good Answer (Score 2)
No more Good Answers.
Randall
Guru

Join Date: Aug 2005
Location: Hemel Hempstead, UK
Posts: 5803
Good Answers: 315
#5
In reply to #4

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

07/31/2023 10:17 AM

GA. I couldn't see an easy way to work it out without counting them.

__________________
 We are alone in the universe, or, we are not. Either way it's incredible... Adapted from R. Buckminster Fuller/Arthur C. Clarke
Reply
Brave Sir Robin
Guru
Hobbies - DIY Welding - Wannabeabettawelda

Join Date: May 2007
Location: Annapolis, Maryland
Posts: 7870
Good Answers: 452
#6
In reply to #4

Re: Counting to 1,000 by 3's (August 2023 Challenge Question)

08/02/2023 4:48 PM

Nicely done without a spreadsheet, not that there is anything wrong with that, but I do have an appreciation for solutions based on logic rather than brute force computing.

Reply
Reply to Blog Entry 6 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:

Brave Sir Robin (1); Randall (2); Rixter (2); SolarEagle (1)

Previous in Blog: Bears and Ferries, Oh My! (July '23 Challenge Question)   Next in Blog: A Deck of Cards in the Dark (September '23 Challenge Question)

Advertisement

Got Something to Say?
Ask a Question
Start a Discussion

Search this Section
General Discussion:
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 Discussion
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 (85 right now)
Show Members
Advertisement