Problem 24 · 2014 Math Kangaroo
Stretch
Logic & Word Problems
caseworksum-constraint
Albin has put each of the digits from 1 to 9 in the fields of the table. In the diagram only 4 of these digits are shown. For the field containing the number 5, Albin noticed that the sum of the numbers in the neighbouring fields is 13 (neighbouring fields are fields which share a side). He noticed exactly the same for the field containing the digit 6. Which digit had Albin written in the grey field?
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Answer: D — 8
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Hint 1 of 3
The grey centre square touches all four edge squares, and the four corners 1, 2, 3, 4 are already filled in.
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Hint 2 of 3
The missing numbers are 5, 6, 7, 8 and 9, and they go in the centre and the four edge squares.
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Hint 3 of 3
Try placing them so that the neighbours of 5 add to 13 and the neighbours of 6 also add to 13.
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Approach: place 5–9 so both neighbour-sum clues hold
- The four corners are 1, 2, 4 and 3; the digits 5, 6, 7, 8, 9 go in the centre and the four edge cells.
- The cell holding 5 and the cell holding 6 must each have neighbour-sum 13.
- The only arrangement that satisfies both forces 8 into the grey centre.
- Answer: 8.
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