## Task 4 - 230734

The following is required of a number:

If you halve the number, subtract 1 from the result, take a third of the result obtained, subtract 1 from this third, take a quarter of the result thus obtained, and subtract 1 from this quarter,

you get 1.

Give every number that meets this requirement! Prove that every number that meets the requirement is one of the numbers you have given, and that every number you have given meets the requirement!
A number $x$ has the required property if and only if it satisfies the equation

$$
\frac{1}{4}\left(\frac{1}{3}\left(\frac{x}{2}-1\right)-1\right)-1=1
$$

This equation is successively equivalent to

$$
\begin{aligned}
\frac{1}{4}\left(\frac{1}{3}\left(\frac{x}{2}-1\right)-1\right)-1 & =1 \\
\frac{1}{3}\left(\frac{x}{2}-1\right)-1 & =8 \\
\frac{x}{2}-1 & =27 \\
x & =56
\end{aligned}
$$

Thus, it is proven that the number 56 has the required property and that it is the only number with the required property.