Cyclic Permutation of Kaprekar Number/Examples/972

Example of Cyclic Permutation of Kaprekar Number

$972$ is a cyclic permutation of the $3$-digit Kaprekar number $297$.

Thus we have:

\(\ds 972^2\)

\(=\)

\(\ds 944 \, 784\)

\(\ds 944 + 784\)

\(=\)

\(\ds 1728\)

\(\ds 1 + 728\)

\(=\)

\(\ds 729\)

and it is seen that $729$ is another cyclic permutation of $297$.

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $297$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $297$