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Fruity Alphametics (Posted on 2009-10-17) Difficulty: 3 of 5
In this set of alphametic relationships, each of the letters in bold denotes a different digit from 0 to 9. None of the numbers can contain any leading zero.
  • 35*(PLUMS) < 2*(MELONS) < 3*(APPLES), and:
  • 16*(APPLES) < 99*(LEMONS) < 210*(PLUMS)
What is the number that is represented by BANANA?

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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Hybrid solution | Comment 1 of 3

I used a mixture of both mind and machine (mostly machine) to conclude that (0123456789) = (ELONUPABSM), thus (BANANA) = 763,636.

I first noted that since 35*(PLUMS) < 3*(APPLES), then 210*(PLUMS) < 18*(APPLES).  Therefore 16*(APPLES) < 99*(LEMONS) < 210*(PLUMS) < 18*(APPLES).  That meant 99 LEMONS were squeezed between 16 and 18 APPLES, leading me to think that 99*L must be close to 17*A.  Then L could only be 1, with A likely 6 or possibly 5.  I ran a program with the constraints L=1 and A=6 to find out that P=5, E=0, and M=7, 8, or 9; trying A=5 gave no results.  I then ran a similar program with these new constraints to find that M=9, O=2, N=3, S=8, and U=4, and therefore the unused B=7.

And that's how I spent my entire Saturday, and I can't think of a better way to do it!

Edited on October 18, 2009, 1:44 am
  Posted by Jim Keneipp on 2009-10-18 01:41:29

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