Answer:
21
Here’s legitimate proof that 9+10=21
(9 + 10) (base x) = 21 (base y)
9(1) + [1(x) + 0(1)] = 2(y) + 1
Simplify and solve for y:
2y = 8 + x
y = 4 + x/2
Since we have number bases, we want x and y to be positive integers. The term x/2 requires that x be a positive even number.
Also since 9 is in base x, we have x ≥ 10, as the digit 9 would not be used for a base 9 or smaller.
Thus we have the pairs of solutions:
x = 10, so y = 9
x = 12, so y = 10
x = 14, so y = 12
…
x, y = 4 + x/2 … Therefore 9+10=21!
