# 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 8521

27% OFF

X

## How Does It Work?

### 1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

### 2. Add to Cart

Add the eBook to your cart.

### 3. Checkout

Complete the quick and easy checkout process.

### 4. Download

Immediately receive the download link and get the eBook in PDF format.

## Why Buy eBook From Effortlessmath?

Save up to 70% compared to print

Instantly download and access your eBook

Help save the environment

Lifetime access to your eBook

Over 2,000 Test Prep titles available

Over 80,000 happy customers

Over 10,000 reviews with an average rating of 4.5 out of 5

24/7 support

Anytime, Anywhere Access