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Ontario Mathematics Olympiad
Sample Question #3NOTE: 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:
Then next he said to ad the two numbers, and finally, erase the two numbers and any digit in the answer.
|342195||>>>||34 ? 282|
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.
Try to find the missing digit in the following numbers:
|5 ? 3086|
|54 ? 028|