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Powerful 9

Age 14 to 16 Short
Challenge Level

Answer: $9$


Look at the last digits of powers of $9$.

  odd                     even
  $9$                          $81$
$729$                    $ 279\times 9 = ....1$
$ ...1\times9=...9$        $...1$
 $...9$                      $...1$

$9^9$ is a power of $9$ so $9^9$ is odd
This means that $9^{9^9}$ is an odd power of $9$, so it ends in $9$.


You can find more short problems, arranged by curriculum topic, in our short problems collection.