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ten - nine = 1 (Posted on 2009-04-23) Difficulty: 2 of 5
Solve this alphametic, where ten and nine are respectively numbers in base 10 and base 9 notation. Each of the small letters in bold represents a different digit, and none of the numbers contains any leading zero.

(ten)10 - (nine)9 = 1

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
If n ≥2, then : (ten)10 = (nine)9 + 1 > (1000)10, which is a contradiction. Thus, n=1, so that:

(te1)10 = (1i1e)9 + 1

-> 100*t + 9*e – 81*i - 738 = 0

-> t = 0 (mod 9)

Since we cannot have any leading zero, it follows that t = 9

Hence, 81*i – 9*e = 162

Or, 9i – e = 18, which gives: (i, e) = (2,0)

Therefore, ten = 901 and, nine = 1210 is the only possible solution to the given problem.

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*** Adapted from JRM 1034 by H. Everett Moore.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionsolutionDej Mar2009-04-23 19:01:07
solutionxdog2009-04-23 13:47:31
solutioned bottemiller2009-04-23 12:40:50
computer solutionDaniel2009-04-23 11:48:49
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