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You can just add the last digit of each number. Whenever you get a two-digit number, you can discard all digits except the last one.

Another alternative is to count how many odd numbers there are - once again, you only need to consider the last digit. If the number of odd numbers is even, the sum is even; otherwise it is odd. (You can ignore even numbers for this calculation.)

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Q: How can you determine whether a sum of numbers is even or odd with out building a tile model or computing the sum?
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