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Spaced Out Cent (Posted on 2008-03-01) Difficulty: 2 of 5
Each of the letters represent a different digit from 0 to 9 in the following alphanumeric subtraction problem:

                                SPACE
                               -  CENT                                
                                  3651

What is the word representing 3651? How about 15631?

Note: Neither S nor C can be 0.

  Submitted by K Sengupta    
Rating: 2.7500 (4 votes)
Solution: (Hide)
SPACE = 13296, CENT = 9645

13296 - 9645 = 3651

The word representing 3651 is PETS.

The word representing 15631 is STEPS.

EXPLANATION:

Since S must be non zero, it follows that S=1. Then, C (under P) is greater than 5.

If C is 6, then P is zero, but N is 0 or 1 in that situation. This is a contradiction.

If C=7, then (P, N) = (2, 3)
If C=9, then P is 2 or 3, and N is 3 or 4.

So, we have the following cases:

Case(i): (S, C, P, N) = (1, 7, 0, 2)
Case (ii): (S, C, P, N) = (1,8,2, 3)
Case(iii): (S, C, P, N) = (1, 9,2,3)
Case(iv): (S, C, P, N) = (1, 9, 2, 4)
Case(v): (S, C, P, N) = (1, 9, 3, 4)

If the carryover from C to E were 1, then T would have been 9 and C must have been equal to N+6. This violates case (iii), which is eliminated forthwith.

E cannot be 1. If E is 2, then T=1 and accordingly, E cannot be 2. If E is 3, then T=2, and so E cannot be 3. Hence E must be greater than 3.

Accordingly, either the carryover from P to A is 1, or C-P = 6. This violates cases (i) and (iv), and accordingly, these are eliminated.

If E=4, then T=3, and so E cannot be 4
If E=5, then A=1, and so E cannot be 5
If E=7, then A=3, and so E cannot be 7
If E =8, then A=4, and so E cannot be 8
If E=9, then T=8, and so E cannot be 9.

Accordingly, E =6. Hence, (A, T) = (2, 5). So, case (ii) is eliminated since A=P=2 is a contradiction.
The remaining case is case (v), which is valid, and so:
(S, C, P, N, E, A, T) = (1, 9, 3, 4, 6, 2, 5)

Therefore, 3651 represents PETS and 15631 represents STEPS and the required alphanumeric subtraction problem when completed is given by:
13296 - 9645 = 3651.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Solution with CommentsK Sengupta2008-03-11 03:54:06
Solution with Commentsed bottemiller2008-03-10 17:35:24
solutioned bottemiller2008-03-10 16:57:48
SolutionSolutionDej Mar2008-03-01 14:44:23
SolutionONE POSSBILITYAdy TZIDON2008-03-01 13:16:41
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