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?

My spreadsheet read something like this and naturally there are embedded formulae.


A E O U L M N P S B
6 7 2 4 3 9 0 5 8 1

P L U M S                        
5 3 4 9 8       (=) 53498
L E M O N S                    
3 7 9 2 0 8    (=) 379208
M E L O N S                    
9 7 3 2 0 8    (=) 973208
A P P L E S                    
6 5 5 3 7 8    (=) 655378
B A N A N A                    
1 6 0 6 0 6    (=) 160606

35*(PLUMS)  <  2*(MELONS)  <   3*(APPLES)                        
 1872430       1946416        1966134        True
                        73986           19718           [values determine T/F]
                        
16*(APPLES) < 99*(LEMONS) < 210*(PLUMS)                       
10486048    37541592         11234580      False
                  27055544        -26307012        [values determine T/F]
                       
Somewhere some values are valid, I expect P=5 is true.

I had decided that P was 5 and A seemed to be 6 while M was 9.  From there I couldn't quite manipulate the numbers properly.
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Seeing Jim's response,
A E O U L M N P S B
6 7 2 4 3 9 0 5 8 1
or
E L O N U P A B S M
0 1 2 3 4 5 6 7 8 9

by replacing my values with his set I concur with his solution.

 

Posted by brianjn on 2009-10-18 01:59:40