Troller, Ver 2.0
The sequel to the popular problem Troller. It is advised you solve the other problem first before attempting this one.
Another woman was tired of people asking her age, so she composed a riddle to hide her real age.
Seventy-two raised to the power of fifty-three
Divide that by seven and the remainder will be
As much as a hundredth of my age times four
Plus a hundredth of my age and the square root of four.
How old is the woman?
The answer is 40.
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1 solution
Note that 7 2 5 3 ≡ 2 5 3 = ( 2 3 ) 1 7 × 4 ≡ 4 ( m o d 7 ) .
Let the woman's age be 1 0 0 x . Then 4 = 4 x + x + 2 ⟹ 1 0 0 x = 4 0 . We are done.