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Let a = 111...1 (n ones), b = 444...4 (n fours), c = 777...7 (n sevens), d = 999...9 (n nines). Find the value of (441a - 81c²) / (14d).

1. 3
2. 5
3. 6
4. 7

Correct answer: 5

Solution

Since b = 4a, c = 7a, d = 9a, the expression becomes (441a - 81*49a²)/(126a) = (441 - 3969a)/126... this makes it depend on a (n), which is odd. Re-reading: likely (441a - 81c²/14d) with operator precedence 441a - (81c²)/(14d) = 441a - (81*49a²)/(126a) = 441a - (3969a²)/(126a) = 441a - 31.5a = 409.5a. That doesn't work either. Most likely interpretation: (441*a - 81*c²) / (14*d) where a has specific digit count making a clean answer. With a = Rₙ (repunit), c = 7*Rₙ, d = 9*Rₙ: expression = (441*Rₙ - 81*49*Rₙ²)/(14*9*Rₙ) = (441 - 3969*Rₙ)/126. For n=1: a=1, c=7, d=9: (441*1 - 81*49)/(14*9) = (441 - 3969)/126 = -3528/126 = -28. Not matching. Try reading as 441*a - (81*c²)/(14*d) is still n-dependent. The question is garbled/ambiguous without knowing n.

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