Question

Question #e7833

Answer 1

I got `12` and `4`.

Explanation:

I have no fancy technique, I just used rewriting and trying things.

Because I see no obvious technique that is applicable, I started by doing some numerical exploration:

`1/3 = 2/6`, but `1/6 + 1/6` doesn't meet the condition requiring different numbers.

`1/3 = 3/9 = 1/9 + 2/9`, but `2/9` cannot be reduced to `1/B` for `B` a whole number.

What have I done? I multiplied by `2/2`, then by `3/3`, so lets try a few more:

`1/3 = 4/12 = 1/12 + 3/12` and that is reducible to `1/12 + 1/4`.

The solution is unique.

We only need to check `B = 1, 2, , . . , 5`

Because if both `A` and `B` are greater than `6`, then

`1/A` and `1/B` are both less that `1/6` and the sum is less than `1/3`.