Number Properties Puzzle – Challenge 11
This is another great math challenge for those who love critical thinking challenges. This puzzle doesn't require advanced mathematical knowledge, just logical reasoning. Let's see how smart you are!

Challenge:
How many positive integers less than 1000 do not have any 5 as any digits?
A- 700
B- 728
C- 736
D- 770
E- 819
The Absolute Best Book to challenge your Smart Student!

The correct answer is B.
Let’s consider 1 digit, 2 digits, and 3 digits numbers separately:
One digit number: From 9 1-digit numbers, eight numbers don’t have any digit as 5.
Two digits numbers: Put A for \(10^{th}\) place and B for unit place. Then, we have AB as a 2 digits number. We can put 8 digits for A (all digits except 0 and 5) and 9 digits for B (except 5). So, we’ll have 8 × 9 = 72 2-digits numbers that don’t have 5 as any digits.
For three digits numbers, ABC: For A, we can put 8 digits (not 0 or 5), for B, we have 9 digits (not 5) and for C, we have 9 digits (not 5). So, there are 648 three digits numbers that don’t have 5 as any digits. 8 × 9 × 9 = 648
In total: 8 + 72 + 648 = 728
The Absolute Best Books to Ace Algebra
Related to This Article
More math articles
- How Does the Process of Renting Books from Online Bookstores Work? A Guide for Students
- Top 10 7th Grade PARCC Math Practice Questions
- How to Solve Arithmetic Series
- 7th Grade NSCAS Math Worksheets: FREE & Printable
- 7th Grade PARCC Math Practice Test Questions
- How to Solve an Absolute Value Inequality?
- 8th Grade OSTP Math Worksheets: FREE & Printable
- Top 10 Tips to Overcome AFOQT Math Anxiety
- 4 Best Printers for Teachers in 2026
- Full-Length CLEP College Mathematics Practice Test
What people say about "Number Properties Puzzle – Challenge 11 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.