Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.

The arithmetic mean of NOD and FIFE is FERN, and:

The geometric mean of NOD and FIFE is FOND, and:

The harmonic mean of NOD and FIFE is FOOD.

Note: For an extra challenge, solve this puzzle without using a computer program.

(In reply to Food by Math Man)

I found that only the first two means were needed to solve this. The harmonic mean then worked out using the only solution to those.

Posted by Charlie on 2012-06-26 17:19:43