Other Topics Puzzle – Challenge 100
A simple math challenge like this one might seem small, but it's a nice puzzle to challenge even a smart student.
Challenge:
What is the greatest four-digit integer that meets the following three restrictions?
1- All of the digits are different.
2- The greatest digit is the sum of the other three digits.
3- The product of the four digits is divisible by 10 and not equal to zero.
The Absolute Best Book to Challenge Your Smart Student!
The correct answer is 8521.
First, notice rule 3 (The product of the four digits is divisible by 10) tells you that one digit must be 5 and none of them should be 0.
Since we’re looking for the greatest four digit integer we need to start with 9, which is the greatest digit. If the first digit is 9, then all the three other digits should add up to 9.
One digit is 5 and there is no 0. Therefore, there are two possible ways:
5 + 3 + 1 = 9
5 + 2 + 2 = 9
None of these solutions work. Because, in the first one, there is no even number and it’s not divisible by 10. In the second one, digit 2 repeated.
Therefore, 9 is not the first digit. Let’s try 8.
If 8 is the first digit. Then:
5 + 2 + 1 = 8
5 + 3 + 0 = 8
The second one has 0, so the only solution is the first one. The number has digits 8, 5, 2, and 1. The greatest such number is 8521The Best Books to Ace Algebra
Original price was: $29.99.$14.99Current price is: $14.99.Original price was: $29.99.$14.99Current price is: $14.99.Satisfied 1 StudentsOriginal price was: $24.99.$14.99Current price is: $14.99.Satisfied 92 StudentsOriginal price was: $24.99.$15.99Current price is: $15.99.Satisfied 125 Students
Related to This Article
More math articles
- Algebra Puzzle – Challenge 45
- What Kind of Math Is on the ACT Test?
- What are the Undefined Limits: Defining from Tables and Graphs
- How to Find the Direction of Vectors?
- Full-Length SSAT Middle Level Practice Test-Answers and Explanations
- Best Cheap Laptops for College Students
- How to Find Asymptotes: Vertical, Horizontal and Oblique
- How to Evaluate Logarithms? (+FREE Worksheet!)
- How To Choose the Right DAT Course?
- How to Prepare for the ASVAB Math Test?
What people say about "Other Topics Puzzle – Challenge 100 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.