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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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