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 Seven Multiple Muse (Posted on 2013-12-23)
Fill up the the 20 empty boxes in the figure shown below, using the 10 base ten digits 0,1,2,3,4,5,6,7,8,9 each occurring exactly twice such that:

(a) Each horizontal number is a multiple of 7.
(b) Each vertical number is a multiple of 7.
(c) The total sum of all the horizontal and vertical numbers is the maximum of all such arrangements satisfying both (a) and (b).
```            +---+
|   |
+---+---+---+
|   |   |   |
+---+---+---+---+---+
|   |   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+
|   |   |           |   |   |
+---+---+           +---+---+ ```
Note: As the figure shows, the bottom row should be considered as two 2-digit numbers rather than a single 4-digit number.

 Submitted by K Sengupta No Rating Solution: (Hide) The arrangements are: Either:``` 7 3 4 3 2 7 6 0 1 9 9 8 2 8 0 5 1 4 5 6``` Or:``` 7 3 4 3 2 7 6 0 8 9 9 8 2 1 0 5 1 4 5 6``` each of them yielding a maximum sum of 10019520. For an explanation, refer to Charlie's solution here.

 Subject Author Date computer solution Charlie 2013-12-23 23:28:37

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