Problem 19 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardcareful-counting
The numbers 1 to 9 are placed in the squares shown, with a number in each square. The sums of all pairs of neighbouring numbers are shown. Which number is placed in the shaded square?
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Answer: D — 7
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Hint 1 of 3
Find the smallest bracket-total first: which two different numbers from 1 to 9 can possibly add up to it?
Still stuck? Show hint 2 →
Hint 2 of 3
Once you know one square, slide along the brackets — each bracket shares a square with the next, so you can fill them in one at a time.
Still stuck? Show hint 3 →
Hint 3 of 3
Keep going along the row until you reach the shaded square.
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Approach: start at the smallest sum, then slide along the shared brackets
- The smallest bracket is 3, and the only two different numbers from 1 to 9 that add to 3 are 1 and 2.
- The next bracket along is 7; the square shared with the '3' pair must be the small one (1) so its partner can be 6, which also fits the 15 bracket (9 + 6) on the other side — so that run is 9, 6, 1, 2.
- Now slide right through the shaded square: 2 + (shaded) = 9 (the bracket of 9), so the shaded square is 9 - 2 = 7.
- So the shaded square holds 7 (D).
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