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.
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