Problem 8 · 2023 Math Kangaroo
Medium
Algebra & Patterns
evaluate-formulaoff-by-one
A straight wooden fence is made up of vertical beams stuck in the ground which are each connected to the next beam by 4 horizontal beams. The fence begins and ends with a vertical beam. Out of how many beams could such a fence be made?
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Answer: B — 96
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Hint 1 of 2
With v vertical beams there are v−1 gaps, each holding 4 horizontal beams.
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Hint 2 of 2
Write the total as a formula in v and see which option it can equal.
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Approach: set up a formula for the beam count
- v vertical beams create v−1 gaps; each gap has 4 horizontals.
- Total beams = v + 4(v−1) = 5v − 4.
- This must equal one of the options: 5v−4 = 96 gives v = 20, a whole number.
- The other options give non-integer v, so the answer is 96.
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