Problem 14 · 2019 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequence
Maxi builds towers made up of little 1 cm × 1 cm × 2 cm building blocks, as shown in the picture. He continues to build his towers in the same way. Finally he uses 28 building blocks for one tower. What is the height of this tower?
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Answer: C — 11 cm
Show hints
Hint 1 of 3
Write down how many blocks each tower in the picture uses, in order.
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Hint 2 of 3
Each new tower adds one more block than the jump before, so the counts grow 3, 6, 10, 15, ...
Still stuck? Show hint 3 →
Hint 3 of 3
Keep extending until you reach 28 blocks, then read that tower's height from how it is built.
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Approach: extend the block-count pattern
- Count the blocks in the picture's towers: 3, then 6, then 10, then 15. Each step adds one more block than the step before (+3, +4, +5, ...).
- Keep going: 15 + 6 = 21, then 21 + 7 = 28, so the 28-block tower is the next one in the staircase pattern.
- Building that tower in the same way, it rises to a height of 11 cm (C).
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