Problem 356

Try to write a formula, which, when any five identical digits are substituted into it, results in 1.

## Solution

When solving these problems, some general considerations can be used. For example, the number 2 can be represented as $(m / m) + (m / m)^{m}$, where $m$ is any number (in our case, from 2 to 9). Another observation is:
if a number $k$ can be represented using only 3 digits $m$, then the numbers $k-1, k, k+1$ can be represented by subtracting, multiplying, or adding the obtained representation of three digits with $\mathrm{m} / \mathrm{m}$.