Problem 1 · 2017 Math Kangaroo
Medium
Algebra & Patterns
work-backwardsubstitution
On the number wall shown, the number on each tile is equal to the sum of the numbers on the two tiles directly below it. Which number is on the tile marked with “?”
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Answer: B — 16
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Hint 1 of 2
The top tile equals the sum of everything fed up from the bottom; write each tile from the bottom two unknowns.
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Hint 2 of 2
Use the known tiles 2020 and 2017 to pin down the bottom values first, then read off the marked tile.
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Approach: set up the wall from the bottom two unknown tiles and use the known tiles
- Call the two leftmost bottom tiles a (the marked one) and b; the bottom row is a, b, 2017.
- The middle-right tile is b + 2017 = 2020, so b = 3.
- The top tile is a + 2b + 2017 = 2039, so a + 2b = 22, giving a = 22 - 6 = 16.
- The marked tile is 16.
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