Question

List all the digit even numbers that can be created by rearranging these number tiles

1
6
5
8

Answer 1

If your teacher is referring to four digit numbers with those tiles, where the tiles cant repeat, then we have 2 choices for the last slot (the units digit). Those two choices are: 6,8.

Recall that a number is only even if and only if the units digit is even (0,2,4,6,8).

Once a choice has been made for the units digit, we have...

• 3 choices for the thousands digit (whatever we didn't pick for the units digit)
• 2 choices for the hundreds digit
• 1 choice for the tens digit

Overall, we have 2*3*2*1 = 12 different four digit numbers possible.

Those 12 numbers are:

1. value = 1658
2. value = 1568
3. value = 5168
4. value = 5618
5. value = 6158
6. value = 6518
7. value = 1856
8. value = 1586
9. value = 5186
10. value = 5816
11. value = 8156
12. value = 8516