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Fill in the following table with 4 digits from 1 to 9 so that the numbers that form comply with the following:
- The number formed by the two digits of row 1 is a multiple of 5 and 3.
- The number formed by the two digits of row 2 is a multiple of 9.
- The number formed by the two digits of column A (read from top to bottom) is a multiple of 4.
- The number formed by the two digits of column B (read from top to bottom) is a multiple of 11.
| TO | B | |
| 1 | ||
| 2 |
Solution
According to condition (1), the number of the first row is a multiple of 5 and 3. If it is a multiple of 5 it must end in 5 or 0, but since there are no zeros it will be a 5, that is B1 = 5.
Condition 4 tells us that the number formed by the two digits of column B (read from top to bottom) is a multiple of 11. Since the number in row 1 ends in 5, then B2 has to be 5 and so both the complete number of column B is 55. That is, B2 = 5
Condition (2) tells us that the number formed by the two digits of row 2 is a multiple of 9, therefore the sum of its figures has to be a multiple of 9, as we know it ends in 5, A2 must be 4 and therefore the full number of row 2 is 45.
A1 it must also be a multiple of 3 (since the sum of its figures is a multiple of 3) and ends in 5, so it can only be 15, 45 or 75, that is, A1 = 1,4,7
Finally, condition (3) indicates that the number formed by the two digits of column A (read from top to bottom) is a multiple of 4 so it must be 14, 44 or 74, the only one of which is multiple of 4 is 44 then A1 = 4.
So the solved crossword puzzle is as follows:
| TO | B | |
| 1 | 4 | 5 |
| 2 | 4 | 5 |
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