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 High Scorer (Posted on 2013-05-21)
```
A     B     C     D     E
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
|  1  |  7  | 13  | 20  |  6  |
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
| 25  |  9  |  2  | 23  | 11  |
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
| 14  | 22  | 17  |  8  | 16  |
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
|  4  | 12  | 10  |  3  | 19  |
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
| 24  | 18  |  5  | 15  | 21  |
+-----+-----+-----+-----+-----+```
Add together five different numbers from the grid above to achieve the highest possible total. Starting at column A and working your way across to column E, only one number may be chosen from each column, and no two numbers may be from the same row or diagonal line.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 3 of 11 |

CLEAR , , 25000
DIM SHARED grid(5, 5), h(5), tot, max, hmax(5), ct

CLS

DATA 1,7,13,20,6
DATA 25,9,2,23,11
DATA 14,22,17,8,16
DATA 4,12,10,3,19
DATA 24,18,5,15,21

FOR row = 1 TO 5
FOR col = 1 TO 5
NEXT
NEXT

FOR r = 1 TO 5
h(1) = r
tot = grid(r, 1)
NEXT

PRINT
PRINT ct
PRINT max
FOR c = 1 TO 5
PRINT hmax(c);
NEXT: PRINT
FOR c = 1 TO 5
PRINT grid(hmax(c), c);
NEXT: PRINT

FOR r = 1 TO 5
good = 1
FOR c = 1 TO col - 1
IF r = h(c) THEN good = 0: EXIT FOR
IF col - c = ABS(r - h(c)) THEN good = 0: EXIT FOR
NEXT
IF good THEN
h(col) = r
tot = tot + grid(r, col)

IF col = 5 THEN
ct = ct + 1
FOR c = 1 TO 5
PRINT grid(h(c), c);
NEXT c: PRINT , tot
IF tot > max THEN
FOR c = 1 TO 5
hmax(c) = h(c)
NEXT
max = tot
END IF
ELSE
END IF

tot = tot - grid(r, col)
END IF
NEXT
END SUB

finds only ten possible choices whose totals need to be compared:

`    Numbers                total 1  22  5  23  19            70 1  12  2  15  16            46 25  12  13  8  21           79 25  18  17  20  19          99 14  7  10  23  21           75 14  18  2  3  6             43 4  7  17  15  11            54 4  9  5  8  6               32 24  9  10  20  16           79 24  22  13  3  11           73`

So the highest total is 99.

The row choice for each column, with its value listed below each, are:

`  2   5   3   1   4 25  18  17  20  19`

 Posted by Charlie on 2013-05-21 17:15:21

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