Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ 1 ⋯ 4 ⋯⟩
⟨ ³ʳᵈa ²ⁿᵈb ⟩, min⟦a,b⟧ = 0
⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
⟨ ⁴ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 205
3rd → a, 0th → b, a+b=2
----- Information -----
🔲 「⟨⋯ 3 ⋯ 1 ⋯ 4 ⋯⟩」
120 permutations match this pattern.
Examples: ⟨314205⟩, ⟨312405⟩, ⟨053214⟩.
🔲 「⟨ ³ʳᵈa ²ⁿᵈb ⟩, min⟦a,b⟧ = 0」
The least element of { [3rd], [2nd] } is 0.
240 permutations match this pattern.
Examples: ⟨354012⟩, ⟨340512⟩, ⟨134025⟩.
🔲 「⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5」
The greatest element of { [4th], [3rd], [2nd] } is 5.
360 permutations match this pattern.
Examples: ⟨352104⟩, ⟨154203⟩, ⟨053241⟩.
🔲 「⟨ ⁴ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 205」
(abc)₁₀ ∶= 100a + 10b + c.
264 permutations match this pattern.
Examples: ⟨514032⟩, ⟨510243⟩, ⟨420315⟩.
🔲 「3rd → a, 0th → b, a+b=2」
48 permutations match this pattern.
Examples: ⟨532410⟩, ⟨452130⟩, ⟨352410⟩.
#125034_v2.3