Four Fours/0
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Puzzle
Using exactly $4$ instances of the number $4$, the task is to write an expression for $0$, using whatever arithmetical operations you consider necessary.
Solutions
Solution $1$
- $0 = \paren {4 + 4} - \paren {4 + 4}$
Solution $2$
- $0 = \dfrac {4 - 4} {4 + 4}$
Solution $3$
- $0 = \paren {4 \times 4} - \paren {4 \times 4}$
Solution $4$
- $0 = \dfrac 4 4 - \dfrac 4 4$
Solution $5$
- $0 = \paren {4 - 4} + \paren {4 - 4}$
Solution $6$
- $0 = \paren {4 - 4} - \paren {4 - 4}$
General Solutions
Let $\map {e_n} m$ be an expression which uses $n$ instances of $4$ to make $m$.
Then we have:
General Solution 1
- $0 = \map {e_2} m - \map {e_2} m$
where $m \in \N$ is arbitrary.
General Solution 2
- $0 = \map {e_3} m - \map {e_1} m$
where $m \in \N$ is arbitrary.