Question

I'm more than 9 dozen and less than the number of days in 4 months. The sum of my digits is 11.

Answer 1

Answer: 92 or 119

in 4 months, 2 months with 30 days per month, 2 months with 31 days per month

suppose: the number to find is X

have: 90 < X < 30.2 + 31. 2 ⇔ 90 < X < 122

if X is a number has 2 digits => X is xy

=>
`\left \{ {{x+y=11} \atop {90<x\leq 100}} \right.`

=> xy = 92

if X is a number has 3 digits => X is abc

we have:
`\left \{ {{a+b+c=11} \atop {100\leq abc<122}} \right.`

because 100 ≤ abc < 122 => a = 1; b = 0 or 1

+) if a =1 ,b = 0 but a+ b +c = 11 => c = 10 (removed because c is a 1-digit number)

+) if a = 1, b = 1 => c = 9

=> abc = 119

=> X is 92 or 119

Explanation:

Answer 2

The answer would be 119

More than 9 dozen (9 x 12 = 108)

And

Less than the number of days in 4 months (4 x 30 = 120 or 4 x 31 = 124)