Problem 10 · 2023 Math Kangaroo
Easy
Logic & Word Problems
Arithmetic & Operations
sum-constraintcasework
Evita wants to write the numbers from 1 to 8, with one number in each field. The sum of the numbers in each row should be equal. The sum of the numbers in each of the four columns should also be the same. She has already written in the numbers 3, 4 and 8 (see diagram). Which number does she have to write in the dark field?
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Answer: E — 7
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Hint 1 of 2
The numbers 1..8 add to 36; use that to find each row sum and each column sum.
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Hint 2 of 2
Fit the remaining numbers around the given 3, 4 and 8 so every row and every column hits its target.
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Approach: use the fixed total to pin row/column sums, then place numbers
- 1 + 2 + ... + 8 = 36; with two equal rows each row sums to 18, and with four equal columns each column sums to 9.
- Place the remaining numbers so each column totals 9 and each row totals 18, respecting the given 3, 4 and 8.
- The dark field is then forced to be 7.
- So the answer is 7 (E).
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