Problem 20 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
sequence-of-figures
Tina draws shapes into each field of the pyramid. Each field in the second and third rows contains exactly the shapes of the two fields directly below it. Some fields are already filled in. Which shapes does she draw into the empty field of the bottom row?
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Answer: D
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Hint 1 of 3
A filled field is just the two fields below it combined, so a field above tells you the total of the pair underneath.
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Hint 2 of 3
Find a field whose value you know that sits right above the empty one, then subtract the shapes you can already see.
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Hint 3 of 3
Whatever shapes are missing after that subtraction must belong in the empty bottom field.
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Approach: use the rule that each field is the combination of the two below it
- Each field equals the shapes of the two fields beneath it, so a middle field is the sum of its two bottom fields, and the top field is the sum of all three bottom fields (with the middle one counted twice).
- Filling in the fields that are already given, subtract the known bottom fields from the totals to isolate the missing bottom field.
- The shapes left over for the empty bottom field are one circle and one triangle.
- That matches answer D.
Mark:
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