If you multiply two whole numbers together, what is the last digit of the answer most likely to be?
Solution to Problem:
If you make a mistake, it could be anything.
But assuming you do it right, the answer is 0.
The last digit of a product depends only on the
last digits of the factors.
Consequently, with two factors, there are 100
possibilities:
0x0, 0x1, 0x2, ... 9x9.
How many of these give 9?
Just four: 9x1, 7x7,
3x3, and 1x9.
How many give 8?
There are twelve 8's. You can readily see this in
a multiplication table:
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 2 | 0 | 2 | 4 | 6 | 8 | 0 | 2 | 4 | 6 | 8 |
| 3 | 0 | 3 | 6 | 9 | 2 | 5 | 8 | 1 | 4 | 7 |
| 4 | 0 | 4 | 8 | 2 | 6 | 0 | 4 | 8 | 2 | 6 |
| 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| 6 | 0 | 6 | 2 | 8 | 4 | 0 | 6 | 2 | 8 | 4 |
| 7 | 0 | 7 | 4 | 1 | 8 | 5 | 2 | 9 | 6 | 3 |
| 8 | 0 | 8 | 6 | 4 | 2 | 0 | 8 | 6 | 4 | 2 |
| 9 | 0 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
There are also twelve each of 2's, 4's, and 6's.
But as you can see from the table,
nothing is close to 0.
There are 27 zeroes, so the
probability of getting a zero is 27/100.
The next closest probability is 12/100.
Correctly solved by:
| 1. Erin McGinnis | Winchester, VA |
| 2. David Powell | Winchester, VA |
| 3. Matthias | Switzerland |
| 4. Kirstine Wynn | Winchester, VA |