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2019 Math Kangaroo

Problem 11

Problem 11 · 2019 Math Kangaroo Medium
Number Theory place-valuesum-constraint

Three five-digit numbers are written onto three separate pieces of paper, as shown. Three of the digits in the picture are hidden. The sum of the three numbers is 57263. Which are the hidden digits?

Figure for Math Kangaroo 2019 Problem 11
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Answer: B — 1, 2 and 9
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Hint 1 of 2
The three five-digit numbers add to 57263; match digits column by column.
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Hint 2 of 2
Work through the addition with carries to pin down each hidden digit.
Show solution
Approach: column addition with the known total
  1. Line up the three five-digit numbers so their sum is 57263.
  2. Filling the columns with the right carries forces the three covered digits.
  3. The hidden digits are those of option B.
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