Problem 6 · 2019 Math Kangaroo
Medium
Number Theory
place-valuesum-constraint
Three four-digit numbers are written on three separate pieces of paper, as shown. The sum of the three numbers is 11126. Three of the digits in the picture are hidden (covered by the overlapping papers). Which are the three hidden digits?
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Answer: B — 1, 5 and 7
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Hint 1 of 2
The three four-digit numbers add to 11126; line them up by place value and use the visible digits.
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Hint 2 of 2
Work column by column from the units, tracking carries, to pin down the three covered digits.
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Approach: add the three numbers by columns using the total 11126
- Stack the three four-digit numbers as a column addition equal to 11126.
- Going column by column from the units and carrying as needed, the visible digits force each hidden position in turn.
- Completing the reconstruction gives the three hidden digits as 1, 5 and 7.
- Answer (B) 1, 5 and 7.
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