geometry n*n

Geometry Level 3

In the * grid table, some isosceles right triangles with 2 sides are placed so that each vertex is the grid point of the grid table. The triangles do not overlap, and each edge of each grid belongs to the inner or boundary of a triangle. Try to find all that meets the conditions.

k 3k 6k+2 2k

Mathem Matics by Mathem Matics , 19, China

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1 solution

Mathem Matics
Feb 2, 2019

η”±δΊŽπ‘› Γ— π‘›ηš„ζ–Ήζ Όθ‘¨δΈ­ε…±ζœ‰2𝑛(𝑛 + 1)村某δΈͺζ Όηš„θΎΉοΌŒζ―δΈͺι’˜δΈ­δΈ‰θ§’ε½’θ¦†η›–ε…ΆδΈ­ηš„ 3 村 于是：3 | 2𝑛(𝑛 + 1) ε³ζœ‰οΌšπ‘› ≑ 0 ζˆ– 2(π‘šπ‘œπ‘‘ 3) ζ–Ήζ Όθ‘¨θΎΉηΊΏθ’«η­‰θ…°η›΄θ§’δΈ‰θ§’ε½’ηš„ζ–œθΎΉθ¦†η›–οΌŒζœ‰οΌš2 | 𝑛 ζ•…θ€ŒοΌšπ‘› ≑ 0 ζˆ– 2(π‘šπ‘œπ‘‘ 6) 𝑛 = 2及 𝑛 = 6 ζ—Άζœ‰ζž„ι€ οΌš

𝑛 = 2 𝑛 = 6

η”±δΈ‹ε›Ύζž„ι€ ηŸ₯：θ‹₯𝑛 Γ— π‘›ηš„ζ–Ήζ Όθ‘¨ε―δ»₯θ’«θ¦†η›–οΌŒεˆ™(𝑛 + 6) Γ— (𝑛 + 6)ηš„ζ–Ήζ Όθ‘¨δΉŸε―δ»₯蒫覆 η›–οΌš (𝑛 + 6) Γ— (𝑛 + 6)

δ»Žθ€ŒοΌŒη»ΌδΈŠζ‰€θΏ°οΌš 当𝑛 = 6π‘˜ζˆ– 6π‘˜ + 2(π‘˜ ∈ 𝒁+ ) ζ—ΆοΌŒη¬¦εˆι’˜ζ„γ€‚

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