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Nod to fife and food (Posted on 2012-06-26) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution answer | Comment 3 of 5 |
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
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