Proposed by Alan Frisch, Christopher Jefferson, Ian Miguel, Toby Walsh

The original fractions puzzle is specified as follows. Find 9 distinct non-zero digits that satisfy:

```
A D G
-- + -- + -- == 1
BC EF HI
```

where `BC`

is shorthand for `10B+C`

, `EF`

for `10E+F`

and `HI`

for `10H+I`

.

A simple generalisation is as follows. Find 3n non-zero digits satisfying: $ 1 = \sum_{i \in 1..n} x_i / y_iz_i $

where $y_iz_i$ is shorthand for $10y_i+z_i$ and the number of occurrences of each digit in $1..9$ is between $1$ and $ceil(n/3)$.

Since each fraction is at least $1/99$, this family of problems has solutions for at most $n <= 99$. An interesting problem would be to find the greatest $n$ such that at least one solution exists. A further generalisation might specify that the fractions sum to $ceil(n/3)$.