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Ontario Mathematics Olympiad

Sample Question #3

NOTE: This was an event for two students.

The Missing Number

The Chinese were wonderfully expert at figures. Here is an example. A Chinese mathematician said to write down any two numbers, provided that in forming them, you used all the digits from 0 to 9 once. For example, you could write:

342195 and 6087

Then next he said to ad the two numbers, and finally, erase the two numbers and any digit in the answer.

342195    >>>    34 ? 282
+  6087

The professor glanced at the number 34 ? 282 and immediately exclaimed, "The missing number is 8".

Can you supply the missing digit in the following, and explain how the Chinese mathematician was able to guess the missing digit in the answer so quickly.

1 ? 1341

Try to find the missing digit in the following numbers:

5 ? 3086
54 ? 028
? 31346
10899 ?