There is a 4-digit number. All the digits are different. The digit in the hundreds place is thrice the digit in the ones place. The digit in the tens place is the smallest odd number. The sum of all the digits is 21. What is the number?
| |
Thousands |
Hundreds |
Tens |
Ones |
Total |
| Scenario 1 |
16 (✗) |
3 |
1 |
1 |
21 |
| Scenario 2 |
12 (✗) |
6 |
1 |
2 |
21 |
| Scenario 3 |
8 (✓) |
9 |
1 |
3 |
21 |
Digit in the tens place
= Smallest odd number
= 1
If 1 is in the ones place and 3 is in the hundreds place
Digit in the thousands place for scenario 1
= 21 - 3 - 1 - 1
= 16 (✗)
If 2 is in the ones place and 6 is in the hundreds place
Digit in the thousands place for scenario 2
= 21 - 6 - 1 - 2
= 12 (✗)
If 3 is in the ones place and 9 is in the hundreds place
Digit in the thousands place for scenario 3
= 21 - 9 - 1 - 3
= 8 (✓) (Digit in the thousands place must be single digit.)
Number = 8913
Answer(s): 8913
