Flowers
The Fairy is trying to give away all of her flowers to 28 girls and 37 boys in such a way that each girl gets flowers and each boy gets flowers.
What is the maximum number of flowers the Fairy can have such that the above condition is met and there is only one integer solution
The answer is 2072.
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1 solution
We get Diofant equation 28x+37y=n, x>0, y>0, x, y are integers. If x, y are solutions for given n, then x-37 and y+28 are also solutions, so we must have x=37and y=28 and n = 2 × 3 7 × 2 8 = 2 0 7 2 .