Problem 20 · 2009 Math Kangaroo
Hard
Algebra & Patterns
evaluate-formula
A pattern is made out of white square tiles. The first three patterns are shown. How many tiles will be needed for the tenth pattern?
Show answer
Answer: D — 92
Show hints
Hint 1 of 2
The white tiles frame the n x n grey block - write the white count as a formula in n.
Still stuck? Show hint 2 →
Hint 2 of 2
The outer shape is an (n+4) by (n+4) square with the four corner tiles missing.
Show solution
Approach: build a formula for the white tiles
- Pattern n has a grey n x n centre inside an (n+4) x (n+4) square with the four corner tiles absent.
- White tiles = (n+4)^2 - n^2 - 4 = 8n + 12.
- For n = 10 that is 8 x 10 + 12 = 92.
Mark:
· log in to save