All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Spaced Out Cent (Posted on 2008-03-01)
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.

 Subject Author Date re: Solution with Comments K Sengupta 2008-03-11 03:54:06 Solution with Comments ed bottemiller 2008-03-10 17:35:24 solution ed bottemiller 2008-03-10 16:57:48 Solution Dej Mar 2008-03-01 14:44:23 ONE POSSBILITY Ady TZIDON 2008-03-01 13:16:41

 Search: Search body:
Forums (0)