Problem 11 · 2014 Math Kangaroo
Medium
Arithmetic & Operations
work-backward
Leo writes numbers in the multiplication pyramid. In a multiplication pyramid, you multiply two numbers that are next to each other to get the number directly above them (in the middle). Which number must Leo write in the grey field?
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Answer: E — 8
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Hint 1 of 3
Each block is found by multiplying the two blocks right under it.
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Hint 2 of 3
Start at the bottom row, which you know, and build one row up at a time.
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Hint 3 of 3
Keep multiplying neighbouring blocks until you reach the grey one.
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Approach: build the pyramid upward, multiplying each pair of neighbours
- Start with the bottom row 1, 2, 2, 1.
- Multiply each neighbouring pair to get the next row up: 1×2 = 2, 2×2 = 4, 2×1 = 2, so that row is 2, 4, 2.
- Multiply neighbours again: 2×4 = 8 and 4×2 = 8, so the grey block is 8.
- Answer: 8.
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