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.

123 56 89
FOE DR IN

NOD  =  925
FIFE = 1813
FERN = 1369
FOND = 1295
FOOD = 1225

FERN = (NOD+FIFE)/2
FOND = SQRT(NOD*FIFE)
FOOD = 2/(1/NOD + 1/FIFE) = 2*(NOD*FIFE)/(NOD+FIFE)

Posted by Dej Mar on 2012-06-27 00:59:35