Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p5, p4, p0} = 2
{p4, p3, p2} = ? + {0,2,3}
Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ5 ³ʳᵈ2 ²ⁿᵈ4 ¹ˢᵗ1 ⁰ᵗʰ0 ⟩ ≥ 2
⛔Avoid
min ⊢4⊣ = 1
max {p5, p2, p1} = 5
----- Information -----
🔲 「median {p5, p4, p0} = 2」
The median of { [5th], [4th], [0th] } is 2.
There are 216 permutations matching this pattern.
Examples: ⟨523140⟩, ⟨420531⟩, ⟨410352⟩.
🔲 「{p4, p3, p2} = ? + {0,2,3}」
{ [4th], [3rd], [2nd] } = { ?, ?+2, ?+3 }.
There are 108 permutations matching this pattern.
Examples: ⟨354210⟩, ⟨052431⟩, ⟨213405⟩.
🔲 「Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ5 ³ʳᵈ2 ²ⁿᵈ4 ¹ˢᵗ1 ⁰ᵗʰ0 ⟩ ≥ 2」
⟨pᵢ⟩ matches this pattern if and only if #{ i: pᵢ = qᵢ } ≥ 2, where ⟨qᵢ⟩ ∶= ⟨352410⟩.
There are 191 permutations matching this pattern.
Examples: ⟨054213⟩, ⟨350241⟩, ⟨243510⟩.
🔳 「min ⊢4⊣ = 1」
The least element of ⊢4⊣ is 1. Also written as B(x=4, r=1), ⊢4⊣ denotes the neighborhood of 4 with radius one.
There are 528 permutations avoiding this pattern.
Examples: ⟨452130⟩, ⟨325401⟩, ⟨105432⟩.
🔳 「max {p5, p2, p1} = 5」
The greatest element of { [5th], [2nd], [1st] } is 5.
There are 360 permutations avoiding this pattern.
Examples: ⟨025134⟩, ⟨153402⟩, ⟨140235⟩.
#125034_v2.7