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Peregrine Rook
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      9514
    +  807
    ------
     10321

\begin{align}9514\\+\quad807\\\hline10321\end{align} As usual, $\text{N}$ must be $1$, because $\text{SAND} \le 9999$ and $\text{BOX} \le 999$, so $\text{NOFUN}$ cannot be more than $19999$.  In fact, it can't be more than $10998$, so $\text{O}$ (letter oh) is $0$ (zero).  From the ones' column, $\text{D+X=11}$, so we carry $1$ into the tens' column and get $\text{U=2}$.

$\text{D}$ and $\text{X}$ can be $3+8$, $4+7$, or $5+6$.  From the hundreds' column, $\text{A+B=10+F}$ (because we need to carry into the thousands' column).  Viable options are $5+8=13$, $6+7=13$, $6+8=14$, and $7+8=15$.  Of those, all but the first eliminate all possibilities for $\text{D}$ and $\text{X}$, so we must have $\text{A}$ and $\text{B}$ $=$ $5$ and $8$.  That eliminates the first and third options for $\text{D}$ and $\text{X}$, leaving us with $4$ and $7$.

<%%>

$\text{A}$ and $\text{B}$ $=$ $5$ and $8$
$\text{D}$ and $\text{X}$ $=$ $4$ and $7$
$\text{F}=3$
$\text{N}=1$
$\text{O}=0$
$\text{S}=9$
$\text{U}=2$

      9514
    +  807
    ------
     10321

\begin{align}9514\\+\quad807\\\hline10321\end{align} As usual, $\text{N}$ must be $1$, because $\text{SAND} \le 9999$ and $\text{BOX} \le 999$, so $\text{NOFUN}$ cannot be more than $19999$.  In fact, it can't be more than $10998$, so $\text{O}$ (letter oh) is $0$ (zero).  From the ones' column, $\text{D+X=11}$, so we carry $1$ into the tens' column and get $\text{U=2}$.

$\text{D}$ and $\text{X}$ can be $3+8$, $4+7$, or $5+6$.  From the hundreds' column, $\text{A+B=10+F}$ (because we need to carry into the thousands' column).  Viable options are $5+8=13$, $6+7=13$, $6+8=14$, and $7+8=15$.  Of those, all but the first eliminate all possibilities for $\text{D}$ and $\text{X}$, so we must have $\text{A}$ and $\text{B}$ $=$ $5$ and $8$.  That eliminates the first and third options for $\text{D}$ and $\text{X}$, leaving us with $4$ and $7$.

<%%>

$\text{A}$ and $\text{B}$ $=$ $5$ and $8$
$\text{D}$ and $\text{X}$ $=$ $4$ and $7$
$\text{F}=3$
$\text{N}=1$
$\text{O}=0$
$\text{S}=9$
$\text{U}=2$

Source Link
Peregrine Rook
  • 4.9k
  • 2
  • 26
  • 40

      9514
    +  807
    ------
     10321