Problem 23 · 2012 Math Kangaroo
Hard
Algebra & Patterns
arithmetic-sequencesubstitution
Stefan has 5 dice in different sizes. If he places them in order next to each other from smallest to biggest then the heights of two neighbouring dice each differ by 2 cm. The biggest die is as big as the tower built by the two smallest dice. How high is a tower made up of all 5 dice?
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Answer: E — 50 cm
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Hint 1 of 2
Write the five heights as an arithmetic list with common difference 2.
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Hint 2 of 2
Use 'biggest = two smallest stacked' to find the starting height.
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Approach: arithmetic sequence
- Let the heights be a, a+2, a+4, a+6, a+8 (increasing by 2).
- Biggest equals the two smallest stacked: a+8 = a + (a+2), so a = 6; heights are 6, 8, 10, 12, 14.
- Total tower = 6+8+10+12+14 = 50 cm.
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