### Brain Teasers

# Mystery Number

Look at the following clues to uncover the mystery number:

1. I am a 4-digit even number, and all of my digits are different.

2. The sum of all my digits is 10.

3. Each of my digits is greater than zero.

4. The sum of the digits in my thousands place and hundreds place equals the sum of the digits in my ones place and tens place.

5. My largest digit is in the thousands place.

What number am I?

1. I am a 4-digit even number, and all of my digits are different.

2. The sum of all my digits is 10.

3. Each of my digits is greater than zero.

4. The sum of the digits in my thousands place and hundreds place equals the sum of the digits in my ones place and tens place.

5. My largest digit is in the thousands place.

What number am I?

### Hint

Make a table with a column for each digit and eliminate the impossibilities.### Answer

The mystery number is 4132.Since the sum of all four digits is 10, and the sum of the digits in the thousands place and the hundreds place is equal to the sum of the digits in the tens place and the ones place, then you know that each of these sums is equal to 5. Because all of the digits in the mystery number are different and none of them are equal to zero, the four digits must be some combination of 1, 2, 3, and 4.

You also know that the ones digit is an even number, so the ones digit is either 2 or 4. Finally, the last clue says that the largest digit is in the thousands place, so the mystery number must be 4132.

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