Puzzle Answer #6
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Continued
from the above page: Thirdly, S is obviously a big digit, which is either "8" or "9"; otherwise, the answer cannot be in 5-digit. |
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| Let S = 8: If S = 8, then 8END + 10RE = 10NEY. In this case, "E" must be "9"; otherwise, the answer cannot be in 5-digit. However, 89ND + 10RE =10,0EY. Since the digit "0" is already taken by the letter "O", it means that "S" cannot represent the digit "8" and "S" should be the digit "9". |
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| Now the problem becomes 9END + 10RE = 10NEY. | ||
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| Next, subtract
10000 from both sides (9000 from 9END, 1000 from 10RE, and 10000 from
10NEY) so that we are down to END + RE = NEY. If END + RE = NEY, then N = E + 1 because ND + RE cannot be less than 100 to make E = N and cannot be more than 200 to make N = E + more than 1. Thus, we have the following: |
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| EED + RE + 10 = EEY + 100 | ||
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Þ |
EED + RE = EEY + 90 | |
| Þ | ED + RE = EY + 90 | |
| Þ | ED + RE - EY = 90 | |
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Þ |
RE + D - Y = 90 | |
| In this case, "R" must be "8" in order to make RE + D - Y = 90. Thus, it becomes 8E + D - Y = 90 or E + D - Y = 10 and the problem now becomes 9END + 108E = 10NEY. | ||
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| Recall
that N = E+ 1, so "E" cannot be 7 because if E = 7, then N = 8,
and the digit "0", "1", "8", and
"9" have been taken. In order to satisfy E + D - Y = 10, "E" and "D" will need to be on the large end and "Y" on the small end. Here are the only possible combinations: |
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| E = 6, D = 7, and Y = 3, so that E + D - Y = 10; | ||
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or |
E = 5, D = 7, and Y = 2, so that E + D - Y = 10. | |
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first combination is not an option because E = 6, then N = 7 and
"D" takes the digit "7" in this case. On the other hand, the second combination will satisfy the whole problem because E = 5, then N = 6. As a summary, we have: |
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| E = 5, N = 6, D = 7, Y = 2, R = 8, S = 9, M = 1, and O = 0 | ||
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| Finally, put everything together, we have: | ||
| S | E | N | D | + | M | O | R | E | = | M | O | N | E | Y | ||||||||||
| Þ | 9 | 5 | 6 | 7 | + | 1 | 0 | 8 | 5 | = | 1 | 0 | 6 | 5 | 2 | |||||||||
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