Puzzles
XYZ
Which digits \(X\), \(Y\) and \(Z\) fill this sum?
$$
\begin{array}{cccc}
&X&Z&Y\\
+&X&Y&Z\\
\hline
&Y&Z&X
\end{array}
$$
Show answer & extension
Hide answer & extension
Both the units and tens columns contain \(Y+Z\). The results are different (\(X\) and \(Z\)), so \(Y+Z=X+10\) and \(Z=X+1\) (because the 1 carries into the next column).
Therefore, \(Y+X+1 = X+10\), so \(Y=9\).
From the hundreds column, we see that \(X+X+1=Y\), so \(X=4\) and \(Z=5\).
Extension
Which digits \(X\), \(Y\) and \(Z\) fill this sum?
$$
\begin{array}{cccc}
&X&Z&Y\\
+&X&Y&Z\\
\hline
&Z&Y&X
\end{array}
$$
