Problem 24 · 2011 Math Kangaroo
Hard
Algebra & Patterns
sequence-of-figuresarithmetic-sequence
Sylvia draws patterns with hexagons as shown. If she carries on drawing in this way, how many hexagons will there be in the fifth pattern?
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Answer: D — 61
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Hint 1 of 3
Count the hexagons in the first few pictures and write how many are added each time.
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Hint 2 of 3
The number of new hexagons added grows by 6 each step: first add 6, then add 12, then add 18.
Still stuck? Show hint 3 →
Hint 3 of 3
Keep adding the next ring, adding 6 more each time, until you reach the fifth picture.
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Approach: add one more ring each time
- Count the pictures: pattern 1 has 1 hexagon, pattern 2 has 7, pattern 3 has 19.
- Each new ring adds 6 more than the last: +6 to get 7, +12 to get 19, so next is +18, then +24.
- Pattern 4 = 19 + 18 = 37, and pattern 5 = 37 + 24 = 61 hexagons, answer D.
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