2024-01-24 Q20

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

2024-01-24 Q20

５４３２１０

－－－－－－

－－０－－－

－－０－－２

－１０－－２

３１０－－２

３１０５－２

３１０５４２

#125034_v2.3