Problem 9 · 2019 Math Kangaroo
Medium
Number Theory
digit-sumplace-value
On each of three separate pieces of paper there is a three-digit number. The papers overlap so that one digit on each of two of them is hidden (see picture). The sum of the three numbers is 826. What is the sum of the two hidden digits?
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Answer: C — 9
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Hint 1 of 3
Line the three numbers up by ones, tens and hundreds, just like in column addition.
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Hint 2 of 3
Add only the digits you can actually see in each column, and call the two covered ones blanks.
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Hint 3 of 3
Compare your visible total with 826 to see what the two blanks together must make up.
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Approach: reconstruct from the column sums
- Stack the three numbers in columns and add only the digits you can see, leaving the two hidden ones as blanks.
- The visible digits already account for most of 826; the gap left over is what the two covered digits must supply together.
- Working through the ones, tens and hundreds columns, the two hidden digits must add up to 9 (C).
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