Problem 4 · 2014 Math Kangaroo
Easy
Number Theory
place-valuedigit-sum
In the addition on the right, three digits have been replaced with a ? (see picture). What is the sum of the three missing digits?
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Answer: A — 0
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Hint 1 of 2
Check the columns of the addition one at a time, starting from the units.
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Hint 2 of 2
The hundreds total is just 1+1+1, so the tens column must add up with no carry into it — that pins down the three hidden digits.
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Approach: read off each column of the column-addition
- Units column: the two known units add to 9 with the third, and the result ends in 9, so no carry leaves the units column.
- Hundreds column: 1+1+1 already makes the 3 in the answer, so nothing can carry into it from the tens.
- That means the three hidden tens digits must add to 0, so each of them is 0.
- The sum of the three missing digits is therefore 0.
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